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Âûïóñê 112 Õàðê³â Õàðê³âñüêèé äåðæàâíèé òåõí³÷íèé óí³âåðñèòåò ðàä³îåëåêòðîí³êè 2000 x풿KBQǿ'($hJ *{8AdАC44PC[ - 4SsK[!X4W{s`Y Њǂ (ɖA $x9GYRz5{4uJz)hϬf։˜v7(FIy7H)>yGtgZXǷpE(~;9XY>-Fjt"XQa#KV U{ VVee?=inQ *W*(qO3;fFRޘ>_[VMXU 5qa6G\k ?dv _VMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:08   (16 2 /z0B(14 |7{KxŜUuB-ȓ%`;X [ҴL@T0N32:?̌h[*F*H;qlȺ.]@lv3v|p{=|Ϲ>,!mW—D99K_,FYzuKn o #,}{wJvhhsSByj?;Jf\tuۗGP>Y-Bk^D$"4Ut/WhMVYW] F1&-+U>_'*Dܣ =ge}t]oz_fffBgy e56 p2;/mtNΖ"~]uީPh!/oZzҙSxpsgUjIi~>ȿbS)>k)lCXg=sSP=_Yr;ԾsS eIlޙ%=? "ٽVX'pgX_364S+{c27locE^xT,SOu~uJ?*1_+z.r;ekSL~R|r1g>uyyu^^VE~M KւS˼Tr3KRK^RI^r<%IyTؼ3!/iKZj^ocypy"j)/7Jd EX. kK-k:]Shk4Njm" ȺSmadj00q݁0"T ï%0LBMEzN^#41yXc6Jt^#\b]\-1^Y^S /|ؘB^t!'nqMo f}Cx vym*x3׈׫Mx J6>/(S&BOG?pTч"Jdԋ V'#&tt8sDRx!+D!6xqo qO"5<[K!WU\-Xby[ Tr(F"=(Q}Be,JvE%&dz EdäzM:=ئ$?Ϛ=&ql/Z"N5Ɗ^9].5X+eTH^VmN~BxiVǙxq(=-)k+-:~#@NF|}8q{Ε -O뵘qqǽ<ݗA_@վyf[GJUw.W&%{Le;$*nG= 'NH8#Ⰶj;%$A˹K:$a3#TyiZYGR)DVZ84 mĖ81_8#r1/1tC^Џ ]\&Wqo̹o!r1'sab-} }q;r_kt0c,5uM]!ޣc58^'ʵ[+=j\O~T:ȓw qv‰9s i1*.(Ua8fEʑ_lb&Cx"b~i&CMG ywb8?bػc6x?_QI <.fzʞVŲѹ'grWOzd{}: NO ㆕+`M Sg/qLCXc gFbiLZtu߼șzg BtoG*1ӯ^cÔ8',S%$|p:q~Xoe8aBPguOw`L\yB5_b#6?eZ}8 AzS'O[/Ѹ{ב\+}Zys7)UXh =ɛ8ڨg~Z}ZţA'EOj5F< cB }iY 5rd%\C5G̍':w/9k{I?8l@mkz#pe~eQ>Q1{ĬKYDŽѐw"#"3=_}V\'"3u ODqW|"6U|x91-D8 A㰑~6Z!G's#C/cvj+w3 lz^/u1(ԅsRQ9G)%9yU9I\sr)'rrcz|_/=-jGJ9IKN6$ᓓ;Dwk$ǺՔ${P3T'u|s"-:In9?Y3AB unΓ-?U;aydQtk_;aw&vl|+Ft긓%2ruA c <|yO5z z!ơy FvxiFx}!R{焱'9'|R\Ύ3]A>\-{RP k}D^쎞|W7To˜zbnpyPliòߩj+2lEwH dt% ?g(c8;>K1zD`y\EWvS@݌E!n#5O.*|d1_0t_YYyѿO]]/WŬ ?Q%cL0 ޞq[X?>C{%G 9Y6^_rlxƾUa\w_+V}xL.;lқ)>< vp͚Bܰk|XP']nrj'2&;Em> Dܩ xE=xWWK<. bV<(~k[)`-#*Dm؝Bרj-2Q&dMA2 uDri63ZC{sM1rGLȰ_m%9ιpU"#Q˖]G' ٣nwš s^V4eWPdA::tO63u |;![-bR-?}U?֭Zہigti{v|򚀼 }SWvG5:,nrqKv֊~M>K!= R2a?9Dܰ>_?G7Ke2Żj2CO}H34svair _|tSk./ 8U媟M~n3tC|w[akQ6wK6 6Gfd|,l~`?vD[DŲgkVœnl5a NUkko(o6 Æ@dv{LkޔvTk~^3y&oW|v"F|ڇ kSk E)G~"[YhHoiwm?8`_uեj.p!þc#.k5ӯVkV)6IVMcs^>Db## Y;;˖wPBO+TWM{n<_>\e Vp}_)g0ډ ;'?-x {S}5#c'⑞K'ql9C.vexPgU;a`iă:q'ǙC }GXmcn|dwӼ<3x6vBƚxs[Ϲc=sK?d:}V<zh:Ym5Oܥs Mʺgo%J-LZ>2>3 |k[Z#F <&χ4'l"3mujnlaRц 蟋㗷3Zwd̋Mاޖ6E:n,bY cN+c}C̱'X>>d?ީןO66 eq1!uTmOsȘuGwx2(oo r?z%-q/GEnxc: Vǁ쵌*B-rZ^՗G_[s>" =5wu '7j߉"XHG'O_^ӻ=q|u1er|wl|-h~jdodr|?T_/voj*5> 5{|Rj^l[kK?qR絪NdĆ&[$+mM)UK;s ?Bd3C ESy&F_zO0W뼕V 3lr{HSs?Gw4>SuUYk5FPCΎﱉcI`fR6#fJV6b-&l$^E:s Zf\lܰWjH’o,,6 2 ÓÄÊ 62-50  ñáîðíèêå ïðåäñòàâëåíû ðåçóëüòàòû èññëåäîâàíèé, êàñàþùèõñÿ êîìïüþòåðíîé èíæåíåðèè, óïðàâëåíèÿ, òåõíè÷åñêîé äèàãíîñòèêè, àâ- òîìàòèçàöèè ïðîåêòèðîâàíèÿ, îïòèìèçèðîâàííîãî èñïîëüçîâàíèÿ êîì- ïüþòåðíûõ ñåòåé è ñîçäàíèÿ èíòåëëåêòóàëüíûõ ýêñïåðòíûõ ñèñòåì. Ïðåäëîæåíû íîâûå ïîäõîäû, àëãîðèòìû è èõ ïðîãðàììíàÿ ðåàëèçàöèÿ â îáëàñòè àâòîìàòè÷åñêîãî óïðàâëåíèÿ ñëîæíûìè ñèñòåìàìè, îðèãè- íàëüíûå èíôîðìàöèîííûå òåõíîëîãèè â íàóêå, îáðàçîâàíèè, ìåäèöè- íå. Äëÿ ïðåïîäàâàòåëåé óíèâåðñèòåòîâ, íàó÷íûõ ðàáîòíèêîâ, ñïåöèàëè- ñòîâ, àñïèðàíòîâ. Ó çá³ðíèêó íàâåäåíî ðåçóëüòàòè äîñë³äæåíü, ùî ñòîñóþòüñÿ êîìï ’ þ- òåðíî¿ ³íæåíåð³¿, óïðàâë³ííÿ, òåõí³÷íî¿ ä³àãíîñòèêè, àâòîìàòèçàö³¿ ïðî- åêòóâàííÿ, îïòèì³çîâàíîãî âèêîðèñòàííÿ êîìï ’ þòåðíèõ ìåðåæ ³ ñòâî- ðåííÿ ³íòåëåêòóàëüíèõ åêñïåðòíèõ ñèñòåì. Çàïðîïîíîâàíî íîâ³ ï³äõî- äè, àëãîðèòìè òà ¿õ ïðîãðàìíà ðåàë³çàö³ÿ â îáëàñò³ àâòîìàòè÷íîãî óïðàâë³ííÿ ñêëàäíèìè ñèñòåìàìè, îðèã³íàëüí³ ³íôîðìàö³éí³ òåõíîëî㳿 â íàóö³, îñâ³ò³, ìåäèöèí³. Äëÿ âèêëàäà÷³â óí³âåðñèòåò³â, íàóêîâö³â, ôàõ³âö³â, àñï³ðàíò³â. Ðåäàêöèîííàÿ êîëëåãèÿ: Â.Â. Ñåìåíåö, ä-ð òåõí. íàóê, ïðîô. (ãë. ðåä.), Ì.Ô. Áîíäàðåíêî, ä-ð òåõí. íàóê, ïðîô., È.Ä. Ãîðáåíêî, ä-ð òåõí. íàóê, ïðîô., Å.Ï. Ïóòÿ- òèí, ä-ð òåõí. íàóê, ïðîô., Â.Ï. Òàðàñåíêî, ä-ð òåõí. íàóê, ïðîô., Ã.È. Çàãàðèé, ä-ð òåõí. íàóê, ïðîô., À. Øòåôàí, äîêòîð-èíæåíåð, Ã.Ô. Êðèâóëÿ, ä-ð òåõí. íàóê, ïðîô., Î.Ã. Ðóäåíêî, ä-ð òåõí. íàóê, ïðîô., Í.Â. Àëèïîâ, ä-ð òåõí. íàóê, ïðîô., Å.Â. Áîäÿíñêèé, ä-ð òåõí. íàóê, ïðîô., Ý.Ã. Ïåòðîâ, ä-ð òåõí. íàóê, ïðîô., Â.Ô. Øîñòàê, ä-ð òåõí. íàóê, ïðîô., Â.Ì. Ëåâûêèí, ä-ð òåõí. íàóê, ïðîô., Â.È. Õàõàíîâ, ä-ð òåõí. íàóê, ïðîô. (îòâ. ðåä.). Àäðåñ ðåäàêöèîííîé êîëëåãèè: Óêðàèíà, 61166, Õàðüêîâ, ïðîñï. Ëåíèíà, 14, Õàðüêîâñêèé ãîñóäàðñòâåííûé òåõíè÷åñêèé óíèâåðñèòåò ðàäèîýëåêòðîíèêè (ÕÒÓÐÝ), òåë. 40-93-97 © Õàðê³âñüêèé äåðæàâíèé òåõí³÷íèé óí³âåðñèòåò ðàä³îåëåêòðîí³êè, 2000 x[lTel ew,5`Rc 6!4DHЭ1Z.Xm0FʋMD|QK+J^FH bl(!7gǓݍ>MgskC"-"2Vn DڣXE<)ߌ}=JfE~1e6rFލ45za@<²YY hr?wj۝/j/}lKp |d:p 74kϭB;9}; ƭ_¯\&7ID-a^,킯ogV馮K"yB WUe5OsfPZ)|Sb[95ǯ}_9MGO7<5<șU7 ~e&P|e<ȳ$1{EEŅVDIX~\YaY~m- khS^F]Vڸ fO{( A-$FG>z9qp#6L+*o$&5r $\ NݻObdbR(,%7O@ϫl$6dLfizwe ~Dp?ic`1h28O<$w}'Y4V܇5Zq~43S۱{@X\㕬O\]f {$IjR$IzpB)?:V6x'؃|ߙg_8z\Fس̽t{YW$=$:kY{/:k{NzNp$Y37)뉽Uye.^(g q-= 5R+~,r!}?1)I;[\~{M~w_7G^N3j1ͩ*ō^l7&^4oNj1FM~Ww|KM3qZ^\&y5[lƼ{mٕrY빼{]ٯuS76_ٿBc&l ~ &L @Y)@0` ODMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:08  %  r%z%(16272h7/< %1m2,[{Cx{UP+ZӴ b-D6$&%aZGjDkyViڴqFG`NsAjL=d{>9R!,\~DO~98"א0p~ŋf\B! #09߲#CxibK)I ¼ps=E]5^ZZsvV7l=7oy uժ7DE1I_(rEF|8S{^P*g-qvsQ~A5lkYˆ sy{Y"0&5A-u1\* 5Ѯ%rZ0fdx虅3B^9fMWmʹSMr|ciG:OmٍanG֑AC]+Oј[_yմ:\Ųh֕kEǧ-{VZz% z%__^w_l_ 63c O~y쪺m _Ҷ_N({/k+\i_%R+d) &^BMNvnoM2Nj5(|v+injvCߕzy>Ἑ8?c6vhuօ5ᅰ!VWKj+g$x'|_i}s!eD8uޛ6+T&x[ /ޣǘkaadh;mݽ{rH'(aT8)~=%1a,:f5˸] l;r47ô2K-Cny}GXr쓓k懻=:ͫ_K7RIŽ4'lv{XwNWjy>Ⴭڟjv@ߩ>X0;'$fE# 㿎i&Y]-i#t=6ypVX+ګ4VȻUA8Gksʒ, %&}C? 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Ðàñ÷åò óãëîâîé ïîãðåøíîñòè ñïåöïðîöåññîðà â ñèñòåìå âèçóàëèçàöèè...............................................4 Äóäàðü Ç.Â., Êàëèíè÷åíêî Î.Â., Øàáàíîâ-Êóøíàðåíêî Ñ.Þ. Î ìåòîäå è çàäà÷àõ òåîðèè èíòåëëåêòà. V............................................11 Áåçðóê Â.Ì., Ãîëîáîðîäüêî Þ.Í. Âåêòîðíàÿ îïòèìèçàöèÿ óñòðîéñòâ ðàñïîçíàâàíèÿ ñëó÷àéíûõ ñèãíàëîâ ïðè íàëè÷èè êëàññà íåèçâåñòíûõ ñèãíàëîâ........................................................................35 Ñâèðü È.Á., Êëèìåíêî À.Â. ×èñëåííîå ìîäåëèðîâàíèå ýëåêòðîãåíåðèðîâàííûõ õåìèëþìèíåñöåíòíûõ ïðîöåññîâ â êàíàëå ñ äâóìÿ ìèêðîïîëîñêàìè-ýëåêòðîäàìè............................41 Àâðàìåíêî Â.Ï., Àëü Ñàëàéìåõ Ñàôâàí, Øòàíãåé Ñ.Â. Îïòèìàëüíîå ðàñïðåäåëåíèå ðåñóðñîâ â óñëîâèÿõ ïëîõîé ñîâìåñòèìîñòè ôóíêöèîíàëüíûõ îãðàíè÷åíèé...............................51 Õàõàíîâà È.Â., Ïóäîâ Â.À., ×àìÿí À.Ë. Ìåòîä àíàëèçà äîïîëíåíèé òåñòà öèôðîâûõ óñòðîéñòâ äëÿ îöåíêè åãî êà÷åñòâà.........59 Ëèçãèí Â.À. Ðàñïðåäåëåííûå ôîêóñèðóþùèå ôàêòîðû è íåêîòîðûå èõ ïðèìåíåíèÿ...........................................................73 Âîðîáüåâà Â.Ï., Ìàðòûíîâ Ñ.À., Ðóäàêîâ Â.À., Õàæìóðàäîâ Ì.À. Ðàñ÷åò ìàãíèòíîé ñèñòåìû òîêàìàêà ñ âàêóóìíûìè ìàãíèòíûìè ïîâåðõíîñòÿìè ñðåäñòâàìè ÑÀÏÐ......................................................79 Ïåòðîñîâ Ä.À., Öóêàíîâ Â.Þ. MISC-êîìïèëÿòîð..........................86 Õàíüêî Â.Â. Còðóêòóðíî-ëîãè÷åñêèå ìîäåëè äëÿ àíàëèçà è òåñòèðîâàíèÿ ñåòåâûõ ñåãìåíòîâ......................................................95 Õàõàíîâ Â.È., Øêèëü À.Ñ., Êîâàëåâ Å.Â. 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ÃÓÑßÒÈÍ, À.Í. ÁÓÃÐÈÉ ÐÀÑ×ÅÒ ÓÃËÎÂÎÉ ÏÎÃÐÅØÍÎÑÒÈ ÑÏÅÖÏÐÎÖÅÑÑÎÐÀ  ÑÈÑÒÅÌÅ ÂÈÇÓÀËÈÇÀÖÈÈ Ðàññìàòðèâàåòñÿ ïîðÿäîê ïðèìåíåíèÿ ìàæîðàíòíîé îöåíêè äëÿ ðàñ÷åòà óãëîâîé ïîãðåøíîñòè ïðîåêòèðóåìîãî ñïåöïðîöåññî- ðà (ÑÏ). Äëÿ êîíêðåòíîãî ïðèìåðà ïîëó÷åíî àíàëèòè÷åñêîå ñîîòíîøåíèå, âàðüèðóÿ ïàðàìåòðû êîòîðîãî, ñ ó÷åòîì çàäàííîãî óãëîâîãî ðàçðåøåíèÿ ñèñòåìû âèçóàëèçàöèè (ÑÂ), ìîæíî ìèíè- ìèçèðîâàòü ìàæîðàíòó è ðåøàòü çàäà÷ó îïòèìèçàöèè ñòðóêòóðû ÑÏ â öåëîì. 1. Àêòóàëüíîñòü è ïîñòàíîâêà çàäà÷è Ïðè ïðîåêòèðîâàíèè Ñ òðåíàæåðîâ òðàíñïîðòíûõ ñðåäñòâ âîçíèêà- åò íåîáõîäèìîñòü ðàñ÷åòà ðàçðÿäíîñòè îïåðàöèîííûõ óñòðîéñòâ, òàáëèö âû÷èñëåíèÿ ôóíêöèé è ò.ï., à òàêæå èõ îïòèìèçàöèè, èñõîäÿ èç çàäàííîé óãëîâîé ïîãðåøíîñòè ãåîìåòðè÷åñêèõ ïðåîáðàçîâàíèé.  ñòà- òüå [1] ïîëó÷åíû ìàæîðàíòíûå îöåíêè òî÷íîñòè ãåîìåòðè÷åñêèõ ïðåîá- ðàçîâàíèé â ñïåöïðîöåññîðàõ ðàñòðîâîé ãðàôèêè â âèäå ñîîòíîøåíèÿ:               МАКС G V F V 5 . 0 , (1) ãäå  – ïðåäåëüíîå çíà÷åíèå óãëîâîé ïîãðåøíîñòè; V – âåêòîð íàáëþ- äåíèÿ; F – ôóíêöèÿ, ñâÿçûâàþùàÿ ïàðàìåòðû òî÷êè íàáëþäåíèÿ è ïîâåðõíîñòè; G – ñêàëÿðíîå ïðîèçâåäåíèå âåêòîðà V ñ åäèíè÷íûì âåêòîðîì n â òî÷êå ïåðåñå÷åíèÿ ïðîåêöèîííîãî ëó÷à ñ ïîâåðõíîñòüþ âèçóàëèçèðóåìîãî îáúåêòà.  ñîîòíîøåíèè (1) â íåÿâíîì âèäå ïðåäñòàâëåíà ñâÿçü ìåæäó òî÷íî- ñòíûìè õàðàêòåðèñòèêàìè âû÷èñëåíèé ÑÏ è óãëîâûì ðàçðåøåíèåì ÑÂ, ÷òî íå äîñòàòî÷íî äëÿ èíæåíåðíîé ïðàêòèêè. Ïîýòîìó àêòóàëüíûì ÿâëÿåòñÿ èçëîæåíèå ïîðÿäêà (ìåòîäèêè) ïðèìåíåíèÿ ïîëó÷åííîé ìà- æîðàíòíîé îöåíêè äëÿ êîíêðåòíûõ ñëó÷àåâ ïðîåêòèðîâàíèÿ ÑÏ. 2. Àëãîðèòì âû÷èñëåíèé è îñíîâíûå ñîñòàâëÿþùèå ïîãðåøíîñòè Ðàññìîòðèì ñëó÷àé, èçëîæåííûé â [2]. Óïðîñòèì ñîîòíîøåíèå (1) äëÿ íàøåãî ñëó÷àÿ. 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Òîãäà: 0 Y F  ; Y Z Z Y Y X X V V n V n V n V n G          ; 2 2 2 Z Y X V V V V    , ãäå ; 23 22 21 C X C Z C V Э Э X      ; 33 32 31 C X C Z C V Э Э Y      . 13 12 11 C X C Z C V Э Э Z      Òàêèì îáðàçîì, ñîîòíîøåíèå (1) áóäåò âûãëÿäåòü òàê:                   МАКС Y Z Y X V V V V Y V 2 2 2 0 5 , 0 . Âíåñåì âåëè÷èíû Y V è 0 Y ïîä êîðåíü: . 5 , 0 2 0 2 0 2 0                                    МАКС Y Z Y X V V Y Y V V Y V (2) Îïðåäåëèì ñëàãàåìûå â ëåâîé ÷àñòè ñîîòíîøåíèÿ (2). Äëÿ ýòîãî êîìïîíåíòû Z Y X V V V , , âåêòîðà V çàïèøåì ñ ó÷åòîì ïîãðåøíîñòè: m m mO V V V    , (3) ãäå   Z Y X m , ,  ; mo V – êîìïîíåíò âåêòîðà V , âû÷èñëåííûé ñ îøèá- êîé; m V  – îøèáêà âû÷èñëåíèÿ êîìïîíåíòà âåêòîðà V . Îïðåäåëèì МАКС V  : МИН Z Y X МАКС Z Y X МИН МАКС МАКС V V V V V V V V V 2 2 2 2 2 2            . Íàèõóäøèì ñëó÷àåì, ïðè êîòîðîì àáñîëþòíàÿ ïîãðåøíîñòü âû÷èñ- ëåíèÿ áóäåò ìàêñèìàëüíîé, ÿâëÿåòñÿ ñëó÷àé, êîãäà âåêòîð V  ðàñïîëî- æåí ïîä óãëîì  45 ê îñÿì X, Y, Z . Ïîýòîìó ìîæíî çàïèñàòü: m m МАКС Z Y X МАКС V V V V V V               41 , 1 707 , 0 3 2 2 2 2 . Âåëè÷èíà V áóäåò ìèíèìàëüíîé òîãäà, êîãäà âåêòîð V íàïðàâëåí ïåðïåíäèêóëÿðíî ê ýêðàíó. Äàííàÿ âåëè÷èíà â ÑÏ ÿâëÿåòñÿ êîíñòàí- òîé è îáîçíà÷àåòñÿ 1 U [2]. Ó÷èòûâàÿ ýòî, âûðàæåíèå äëÿ МАКС V  ïðèìåò âèä 1 41 , 1 U V V m МАКС     . +x pTۄL&l^[PC RI@3PSK+ӴvbP#LX!(h1X|J)Ka@ ;f_g{e ,өu7s܏s=}y1."f Od%%"%3aL5q~Y͡ݣ S!C]VtNd%]jߔ 堕!=чL2\n>+ VY%RM5RrcD-Y=%Y2Dr_@tyy H-6F#$,|2t eG|AYBLK92S'/ת_Z~|Iy^"ƐT eIbӜ4<#U£/EvZ\k r02M> _}i<[l?!EqT~~:$'?3Sݬ#C?UN< я@vԱ [yMĺ-[Kr]N:7+MTGNROsEH@m%O{\EXD-GU)X:ȑ6K 8)~ڠ|*?3{=WR,2;y M蘗6onڶmݽqwb] Vw}"gF%4߫D>bZκ7i58L_H"RL)@i`nJ-Rl\_mVEʐ İTml.$_mC*lg|k v )#-EMճ7F\XKt>8H"y+R$|ݟ-cDd$$y/󐽜2H%Ds,uhgӿXުϸ 2/\`'%bYo<V8\&?u-1B>}Mb ٳ[m#A_k2ъF58Z7FmD/Sw 2KZcԭۃmzbzXv /DwuW1MۭX&?޺ɉaH#yi=;x}#G @$Mf FJoeyOi|)!k;OJ᠂M&WAE{J-k~ߊafM:L'LO.J; /`57A gpP9dOAޣs=LpPVw^-jS:AA~jxGWONsPR)$I2v -w- 1ܔQul&!:h4j&yTmFԨsnj5&`ߗoWn騿*Sn섣rs_C]ϬͣM"i`THc t0r]|L Քˢfp=He9DƳe<؀d"#迌^L%Wǝ%nC7#eoUwɅȔu0N :rr)pr-z.Xlbm;[W<#y9 zg;~Nrjyy@w?t;v9/WWmXnѝr:rp.کpޘYعؾrXWa1#GxX8_j3Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:09  R =(16F2|/ 1@ J:{TIx E;1  Bs1"J|_WBq7à Y#QqdfuVGWaׯ" 7+@AA_wϭ۷>7vnz}>$@aIr§wH~bL9;IZǿodRc%tPX]$IrN3C#S;3%g'-7%(K^{%ʘK>UipTo(R8J7*~0R" .¤]kn?o}ٲeKҗߓ{~OŖ,e%gW"Q֭̔5W$-}Vzbi&s¤9$5棦]q͞OICv[ꉝ6NeɻzF2P_neKr-SvVT}Rէ R2m'U1k'[eԽ"%͟3%m8}eBչ /x;])kczWKߏ%>g]?4 v<}/}ѻvx)eUFc0+Be,qS +g|m Ϙvxf>Ӕ_1._~ 5z\.b\LO6c"7/2ENT̸dO%3!Cl<Ḝ-SR`\ϸ$f\lRۼ XR>Y 㒲_+0b5dCrO1/y"yD'O%<3v k]b) vӊҋ5ky VUMJ猚$ڋ_i|ysA'Äs.Zӗ sg $㔗 O=՗\s^wԹy7ӗ,bRsB/Ҭ{s>"?9^$|lu»>Ht8Ezʻ$9ϖI/P"ʳY/{"%; b p"k%6!r6}iݐ<,[Ay vH/m{ڌNWF 3Q˩ý{pgl{`HO| 45s;< oP#;(Njf)y4YC솔NdsJMJg=T9 kzCrhFE{^uAO@_o>u[=gXjG< Sxi]ܠ.s cpG=#c^=[Zw):1>TYfd{<Y#fx\D !=8,'}>uK_i3?CAW]qӊORLh|+p.~ʦL>슥 ցXWTgޮ1+nffWdήmr&C#ʋ07#& {]KlWY΂NvuvmF1=^.~6혝?%\Xk=zOq~?2 |\*JI!uI*aY3MgH^!$S<=e+5kpTph e,^ۉ:#PL4r.4ڬ<|Iナ')/kAyV^F fP*hRڠ-FA[JVˁ>sN>ea9\䓶t>U)/-w*b8߲eʫ-1[KdH ݉s;k/d^~F5->ޕNy<-zC~m/{ɣP6ޥElޡ|Z_x@D_[1^, VkO5mpv'kƎ&pύz-=>ҝ|8w~t ˑbϦU̕*r[(iʐӌA4-[h&C ݭTW@N";c2ru\Bq(_ozS%_ӄ^҉-_|kv?1B|}֋=%^Y3wKu+k.CpdM#]&_ͯt+{PwVik{ZcSrdTZccB'(_)Coe*C]JZ=WlZ[lV/Z1=j+k-XۮQ4Юds<QƣQ<ェ]#vSw,ZYA?_Q~,1i%g?Xs<XZ<60tU .o.S}iVޑ ܗOC \QWc06zAҾ\|5:i !{h=Wqjh= l/K +lI/T8Vav{/g+C_cn)]|xH:źdo/ZW-xS?|LPtѺk(NjO~z[6g%uTO!N_F}Y'>hU}Ɇ;;SH.R⸮xgTϥ|Ϻ"N:6s m~Y!N8/갾JfuQNtr:u ŴT=iFx*5>~BxY\̖Mu}:=mtkAO݌}Cԭ Kר{hRvR|_oycyn=F{<]|yQf/`O4#u?-('IţA]|ϿC3 m }1 z/W`8O.>zms+<1't 7Xlơ\7{Xߋ{/}h{/?|zPѷe|UˉOF=?;?zc@j)us6ZuՍ}Ad_JWܾ_;+6W_ (x{4J 2 Å{4OĞq\ p{4?^ h{4SfO ɱl}댙:?'t֧6 r1#L>p.3tC_0q;OY~.W't|.ӛxM~9?| ,iğ6&?@|h|Y4旖&:m[ί9;O.M{e} U%0in{Og<^ ey<8iuo9 QnjW;{ݳՑ%TOW?>[eRk\oW`mpv7g^} %j=P5}я-GC~A/U|k e| P#g,_o?!;j^⸿)?Jc N&m3כu1¯*3Ú,YԾcں]^A7Ӊ_:Gg( ^1g[?RL{ }Of+Ў2{ZQ)CGrQ%݉:L=}C}'Uۋ>6T#Wʬ}Y}-PclT5>vc/J?Ǡwh|QW D#"xYOGƋ.)c<4yY_\Q+;@/c \V&Bj;}[ ׿}Q3B}:ǶZ?㷖|:?S.׋RjF#-t6Uc7hK_nP?7A?e)~_k]>ȓD|}/e roV#cW*~yOُygCwlO!pxc qggxkM>~:tN>}!2{N|s^>en[*^nL* z8oftϾL5)'2ߗ/<"<|g:6 -&>KE@I-ތ< ӾG]5 yOl\pOmqo\?)# ci/)BQ/G(f + 8}Kfwi(/!](] p>?O_}{7)2Ќ ci_&=oRhSzL;zA72ؑ{hĽ?ߛ' c}R%‰9KH36mˮQӺ'6UTy6~Bǝ$ٷFOVy%8f+M`j:Js̶RyļE;yh//s~gSZW˾is蛘V+}qe\W^KTLz_|dm컴)l1[;\. de1enud dCC|ėU2ߔ7&oLmT-EKX"H2; ۉ}=EgyO}۷͉7~lsHz;tXF[>N<[̣©^7E˿= ےS ~~ +/?ؿ\鼖rZPUۜ[ئ4~'@O ʸ7t7,i 1~ m鞺 ʁց4&Ϣo܆/x#PnX` ohRNjī+[kw*mJ9߀eTC'H>18lGՂSUQw+~/H=˴o>W^2t <3yn~ .p ~3oW"fb]>"$~PuݜIߦybz#L/ ڶЮdl4GZкyJݦW~2Uc(l-:\z^ Џۿ*.W@-^-Z_Z0U  6jrc|k~A ݩS_.k*M\oOM\>W^5={BH7-WkncMܠֱJD . )1\'T&[Oӧ dzlOݼOOt xOO=\'ҝSl8B)&dJ}u]7 V!?B~. ڷqLޅ!ib@ .ķt~+_D-ud_Fͳlo'Zgus.zo'nS/\ۉ/,_qR#nی;? 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Åñëè ïîëàãàòü, ÷òî âäîëü ñòðîêè ÷èñëî ïèêñåëîâ ðàâíî Z N , à ÷èñëî ñòðîê X N , òî âåëè÷èíà ïðåäåëüíîé àáñîëþòíîé ïîãðåøíîñòè êîìïîíåíò âåêòîðà V â ïèêñåëàõ ðàâíà: L X Z m N N V            2 2 . Îêîí÷àòåëüíî äëÿ МАКС V  çàïèøåì: L X Z МАКС N N U V           2 2 41 , 1 1  . (4) Ðàññìîòðèì â (2) âòîðîå ñëàãàåìîå. Îïðåäåëèì äëÿ Y Z V V Y 0 è Y X V V Y 0 îòíîñèòåëüíûå ïîãðåøíîñòè, êîòîðûå âîçíèêàþò ïðè âûïîëíåíèè îïå- ðàöèé óìíîæåíèÿ è äåëåíèÿ ñ ó÷åòîì ïîãðåøíîñòåé îïåðàíäîâ. Îáî- çíà÷èì ýòè ïîãðåøíîñòè Z  è X  ñîîòâåòñòâåííî.  íàøåì ñëó÷àå âû÷èñëåíèå ýòèõ êîìïîíåíò âûïîëíÿåòñÿ ñ èñïîëüçîâàíèåì ëîãàðèô- ìè÷åñêîé ñèñòåìû ñ÷èñëåíèÿ ïî ñëåäóþùèì ôîðìóëàì [4]: ) ( ) ( ) ( ) ( ) ( 0 2 2 Y Z Y Z O V M V M V P V P Y P Y Z V V Y       , ) ( ) ( ) ( ) ( ) ( 0 2 2 Y X Y X O V M V M V P V P Y P Y X V V Y       , (5) ãäå P è M ñîîòâåòñòâåííî öåëàÿ ÷àñòü (ïîðÿäîê) è ìàíòèññà ëîãàðèôìà ïî îñíîâàíèþ 2 âåëè÷èí Z Y X V V V Y , , , 0 . Ïîñêîëüêó ìíîæèòåëü 0 Y îñòàåòñÿ ïîñòîÿííûì â òå÷åíèå îáðàáîòêè îäíîãî êàäðà èçîáðàæåíèÿ, òî â ñîîòíîøåíèÿõ (5) ÿâíî ïîêàçàí òîëüêî åãî ïîðÿäîê   0 Y P , à ìàíòèññà ââåäåíà â êîýôôèöèåíòû j i C , âåëè÷èí Z X V V , , ÷òî ïîçâîëÿåò îïåðàöèþ óìíîæåíèÿ íà 0 Y çàìåíèòü îïåðàöèåé ñëîæåíèÿ è ñäâèãà. Òàê êàê âû÷èñëåíèå ïîðÿäêîâ âûïîëíÿåòñÿ ñ íåîáõîäèìîé ïîëíîé ðàçðÿäíîñòüþ (ò.å. áåç îøèáêè), òî â äàëüíåéøåì âñÿ îøèáêà îñòàåòñÿ ñîñðåäîòî÷åííîé â âû÷èñëåíèè ìàíòèññ ëîãàðèô- ìîâ è ñîîòâåòñòâóþùèõ èì ïîêàçàòåëüíûõ ôóíêöèé. Îáîçíà÷èì: Z Z M P P Z 2 2   , X X M P P X 2 2   , ãäå ); ( ) ( ) ( Y Z O Z V P V P Y P P    ); ( ) ( Y Z Z V M V M M   ); ( ) ( ) ( Y X O X V P V P Y P P    ); ( ) ( Y X X V M V M M   . 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Òîãäà ) 2 1 2 1 2 2 ( 2 2 1 Z Z ZO Z ZO Z ZO Z Z M Z P P M M P P M P e Z             , ) 2 1 2 1 2 2 ( 2 2 1 X X XO X XO X XO X X M X P P M M P P M P e X             . Äëÿ ðàññìàòðèâàåìîé ñèòóàöèè ðàçíîñòü ïîðÿäêîâ 0     X XO Z ZO P P P P . Ïîÿñíèì ýòî. Íàëè÷èå îøèáêè ìîæåò ïðèâåñ- òè ê òîìó, ÷òî â äðîáíîé ÷àñòè ñòåïåíè O X Z M ) , ( ïîÿâèòñÿ öåëàÿ ÷àñòü, ðàâíàÿ íå áîëåå åäèíèöû. Îäíàêî ïðè âû÷èòàíèè ) , ( ) , ( X Z O X Z M M  , âñëåäñòâèå ìàëîñòè îøèáêè, åäèíèöà áóäåò èñêëþ÷åíà. Òàêèì îáðàçîì, îøèáêà íàõîäèòñÿ â äðîáíîé ÷àñòè M , à öåëûå ÷àñòè ñòåïåíè ðàâíû. Ó÷òåì òàêæå, ÷òî îòíîøåíèÿ Z M Z Z e 1 1 2   , X M X X e 1 1 2   – îòíîñèòåëüíûå ïîãðåøíîñòè òàáëèöû ïîêàçàòåëüíîé ôóíêöèè. Ïðèíèìàåì ) , ( 1 1 1 X Z макс     , è òîãäà 1 1 2       Z ZO M M Z , 1 1 2       X XO M M X . (6) Ââåäåì îáîçíà÷åíèå Z Z ZO E M M   , X X XO E M M   , ãäå Z E , X E – ñóììàðíàÿ àáñîëþòíàÿ ïîãðåøíîñòü âû÷èñëåíèé ñòåïåíè ïîêà- çàòåëüíîé ôóíêöèè. Íàéäåì ñëàãàåìûå Z E è X E , ó÷èòûâàÿ, ÷òî     Y Y Z Z O Y O Z ZO e V M e V M V M V M M       ) ( ) ( ) ( ) ( ,     Y Y X X O Y O X XO e V M e V M V M V M M       ) ( ) ( ) ( ) ( , ãäå Z Y X e e e , , – àáñîëþòíûå îøèáêè ëîãàðèôìèðîâàíèÿ Z Y X V V V и , . Äëÿ íàèõóäøåãî ñëó÷àÿ èìååì ) ( Y Z Z ZO e e M M    , ) ( Y X X XO e e M M    , ò.å. Y Z Z e e E   , Y X X e e E   . Ñ ó÷åòîì ïðèâåäåííûõ ñîîòíîøåíèé ñâåäåì (6) ê âèäó: 1 1 2       Y Z e e Z , 1 1 2       Y X e e X . (7) e6x t7"Y&0 YB! 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J͚جI͚ w\No֤fM l֤R6lxc~&6kR`& gΚ߬I͚جIjM l2T/͚جIfMħ>:N*\R>lb'̱?cZ73ofwof7fKoa`oS9lPCN5"slɸSɜ~1a97ߙ)d̙9w*M`9`;*v@Ȝ!̉[7T2'nlS-Ȝ97T22>Ar{V؁x--3ߢx-FĊX1Sa~z3Y%yy޾8QUeiGw`nvlj'7<6lkyuv޾X?/>}Dγ?3h?0ȋ,,9 Ñ ó÷åòîì ïðèíÿòûõ îáîçíà÷åíèé èìååì: 2 2 22      МАКС Y e ïðè 1  МАКС Y â òàáëèöå. Îêîí÷àòåëüíî 2 2 44 . 1      m V e . (11) Ïîäñòàâèâ (11) â (8), ïîëó÷èì:   1 2 44 1 4 1          m ) X , Z ( V . . (12) Âîçüìåì íàèõóäøèé ñëó÷àé, êîãäà ïðîåêöèè âåêòîðà Y X V V , áóäóò ìàêñèìàëüíûìè è ðàâíû M V . Òîãäà, c ó÷åòîì ïîãðåøíîñòè èçâëå÷åíèÿ êîðíÿ [5], âòîðîå ñëàãàåìîå â (2) óïðîùàåòñÿ äî ñëåäóþùåãî âèäà:                     2 0 2 0 2 25 , 0 Y V V Y Y M  . Äàëåå ñ ó÷åòîì òîãî, ÷òî âåëè÷èíà O Y ïðåäñòàâëÿåò ñîáîé êîíñòàíòó, à òàêæå ñ ó÷åòîì ñòåïåíè [5] è ñîîòíîøåíèÿ (12) èìååì: ) , ( 2 25 , 0 2 0 2 0 X Z Y M Y M макс V V Y V V Y                                   . (13) Ïîäñòàâèâ (4) è (13) â (2), ïîëó÷èì: Разрешение экрана N Z x N X L  1  2 Расчетная угловая погрешность Предельная угловая погрешность  24 2 -15 2 -16 0,000119 25 2 -15 2 -15 0,000107 26 2 -14 2 -15 0,000121 640х480 27 2 -14 2 -15 0,000112 24 2 -16 2 -16 0,000121 25 2 -15 2 -15 0,000115 26 2 -14 2 -15 0,000125 800х600 27 2 -14 2 -15 0,000114 24 2 -17 2 -17 0,000126 25 2 -15 2 -16 0,000106 26 2 -15 2 -15 0,000100 1024х768 27 2 -14 2 -15 0,000117 25 2 -15 2 -16 0,000121 26 2 -15 2 -15 0,000108 27 2 -14 2 -15 0,000121 1280х1024 28 2 -14 2 -15 0,000112 2 -13 =0,000122 Z"xX LUe~%+E1$c2K鴩)VZ&֒L, 6ӶjksYn,K$sjek-\q΁s. ֹ۳=y}ν*oFrLVma0;'hKjq1L@[^du~6uu;aqu؈bFύpacp!Q*.zPcH[  gbW@6Q͵E,Í (+$ЋrTzED)=0 :#ұ%XƘAb}6Յwkc/ 'S#W?͸)IX@MħkNl&'!kIPSID sy\!h4 WE $>650O=Q˞ +Я K丑O'{.#',QN.YesL1^D}E@޳|l_ұ5]1Gw+/Z WWĒrbq|FS Q1ڊXEg8ku0ᔉ-J'9H9º7Ci?1+\8.~.3iGs+:HGjKo rl$W c5yZ4k#ke̽ ko$ {x ]Uyτ$$!P LLHAaxHmaإ5vEQY5ѴUWTQY *jҢN^d<& Jd}w}^zSRg}~}:-˲ke)|fRhoY־,*/}yY֖],{-SaiAwe*oCVgweoޞ-* oޭf*P^ᴲK)ߤ,;m/xiWeW}ydž6yhhW١OygzIv-[pW6t\;lu_]KriᷢgS&;*_)w[ėĢmޕ]Y̯ڞ6vh: -+GY X2)A!&+&W8BcH7{bB-]*=SHKCuon.i@7;vIlusCH؝ݤ'Iںy=Į' }#G)37W&1ILȥ۲uQxsT'A{[DTA`څUoG_jtȝ~s%fҝ|۲gw7ve |UEN$s}[Ojֺӯ'ܕ |B+[siRG>.;w Ȳ[Nڕ]RWg/^_hqfe._{ uo1_c| .GnnCeprM% C|ם/^wQ˨u SЁ8VwZz'ݬYIkFv]C~GK]rc<ڟ,w#T5BN 3Zz>t)OZwNz:V|'OȲQ4O1%?}>b?F~<}J뎒/fTѓtEGǪ9Pm&pVǝכub~S;V\<5)fx،'Ki b%?dکٱʮ^VR ֯]( >.8t>(/sVt~"uR)t=+cr )Ɵ;77^ gsֽ|ӯe:+;z8Yl;u+!}L|xA:لݥb|]@{ ׹ZsC|mOS:;#Eҳ~Str˺n` P! xOSvVC[MdٖmG){2ۘ gS6ɶ5.໳vNw$ugGGI&gg(hےUtw4 .wR`] IC9nxM9Ӄw< e?;Fxheh;<,,˲DݢG_EߠT*OOO3d?OWxjU0iUW-XUYv=ҬGK;YZYUZnQCy(;+F=@/,W ra,]>Pt̩@]F 3YzFO,^W|[G .W8Szd=Q Y%Wl5E̽]Κ0ok7~tֳOGor~4[w?z,(oSIw9{>yO3_1R,Gg.n@?l~y_F>X^ȇߏRdž}lˋYh;<=[:MǤ)W|K~} ܾ$ؾEt' }%u:E]O+j4#51q{O2SCFվ7?M! ȓEl-/Dߢ{#9ibȫ;_cR"Y^䟮ΕV%?ګGg۴Z{Nt]ʎp4Ûfڈ/IirOe;)37uZٚD2|~^(x=uǾGeht`e'+OBG}0*aj=;߫=#J;'ϮiN'-{^? 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[ls@%j%ag\MC6W8~1W=E;3; 8q\^JNVjl5;g>{oxjRC8M8_8x.Q8,8^c|1>m,qJ|<Tk~Xh[q+"qcXd2yKY+,,A 11 ÓÄÊ 519.7 Ç.Â. ÄÓÄÀÐÜ, Î.Â. ÊÀËÈÍÈ×ÅÍÊÎ , Ñ.Þ. ØÀÁÀÍÎÂ-ÊÓØÍÀÐÅÍÊÎ Î ÌÅÒÎÄÅ È ÇÀÄÀ×ÀÕ ÒÅÎÐÈÈ ÈÍÒÅËËÅÊÒÀ. V Ðàññìàòðèâàþòñÿ ïðîáëåìû ïîñòðîåíèÿ ýôôåêòèâíîãî ìà- òåìàòè÷åñêîãî àïïàðàòà äëÿ ôîðìàëèçàöèè è ìîäåëèðîâàíèÿ ìå- õàíèçìîâ èíòåëëåêòà. 5.1. ×èñëîâàÿ èíòåðïðåòàöèÿ àëãåáðû èäåé  [1] áûë ðàññìîòðåí ðÿä èíòåðïðåòàöèé àëãåáðû èäåé.  ýòîé ñòàòüå îïèñûâàåòñÿ åùå îäíà èíòåðïðåòàöèÿ àëãåáðû èäåé, íàçûâàåìîé íàìè àëãåáðîé ÷èñåë . Ê àëãåáðå ÷èñåë ïðèõîäèì, çàìåíÿÿ ýëåìåíòû êàíîíè- ÷åñêîé àëãåáðû èäåé èõ íîìåðàìè.  òàáë. 5.1 ïðåäñòàâëåíû â âèäå ïðèìåðà îïåðàöèè äèçúþíêöèè èäåé (â äàííîé èíòåðïðåòàöèè – íàòóðàëüíûõ ÷è- ñåë) ïðè n =1, 2 è 3. Ìîæíî ñ÷èòàòü, ÷òî òàáëèöåé 5.1 çàäà- íû íåêîòîðûå ôóíêöèè 2-, 4-, è 8-çíà÷- íîé ëîãèêè [2, ñ. 35]. Ïðè n =1 ïðèõîäèì ê òàêîé àëãåáðå ÷èñåë, äëÿ êîòîðîé ðîëü äèçúþíêöèè èäåé âûïîëíÿåò îïåðàöèÿ äèçúþíêöèè äâóçíà÷íîé ëîãèêè. Îäíàêî ïðè ëþáîì n >1 îïåðàöèÿ äèçúþíêöèè èäåé â àëãåáðå ÷èñåë íå ñîâïàäàåò ñ äèçú- þíêöèåé n 2 -çíà÷íîé ëîãèêè ), , max( y x y x   ïîñêîëüêó â àëãåáðå ÷èñåë ëþáîé ðàçìåðíîñòè n >1 1  2=3, à â n 2 -çíà÷íîé ëîãèêå 1  2=2. Èìååòñÿ âàæíîå îòëè÷èå ñåìåéñòâà âñåõ àëãåáð ÷èñåë îò ñåìåéñòâà âñåõ ìíîãîçíà÷íûõ ëîãèê ñ îïåðàöèåé äèçúþíêöèè. Îíî ñîñòîèò â òîì, ÷òî àëãåáðû ÷èñåë ìîãóò áûòü çàäàíû ëèøü íà ìíîæåñòâàõ, ñîñòîÿùèõ èç n 2 ýëåìåíòîâ. Ìíîãî- çíà÷íûå æå ëîãèêè ìîãóò áûòü çàäàíû íà ìíîæåñòâå ñ ëþáûì ÷èñëîì ýëåìåíòîâ k . Îïèøåì íà ÿçûêå àëãåáðû êîíå÷íûõ ïðåäèêàòîâ â ôîðìå íåÿâíîãî çàäàíèÿ [3, ñ.68] îïåðàöèþ äèçúþíêöèè èäåé äëÿ n - ìåðíîé àëãåáðû ÷èñåë. Ñ ýòîé öåëüþ ââåäåì ïðåäèêàò 0 0 0 0 ) , , ( z y x z y x P  (5.1) у 0 1 2 3 4 5 6 7 0 0 1 2 3 4 5 6 7 1 1 1 3 3 5 5 7 7 2 2 3 2 3 6 7 6 7 3 3 3 3 3 7 7 7 7 4 4 5 6 7 4 5 6 7 5 5 5 7 7 5 5 7 7 6 6 7 6 6 6 7 6 7 7 7 7 7 7 7 7 7 7 Òàáëèöà 5.1 x  xmheǯ92KpNsm%R:]ITJ/IDf(_&$AX}(PZ{lKkRB%!9w>-b(e]e ma Ƚq/$SNI[L5`˵vdZ'bKlwGn|4d XC)rIfK|m e)R"T Yye 3EvX2UԩuY{j)".Gߟ!=D̯Rj4$OP_/8kĶB%Vv3Mڨ^)5b`+~3r9`^V ZvVjWH̑jQS-1S%sf>7?ٖ*6D^S&WL \-2CGp=F GodOߒiz!v}-ufoUވ3;]`'w S p3tړ}`3؎nYG'89pĈ6Vչo%'٣3ؖArd&z z!q@s% um"n {}~ ;P4Ż _úwZЂ.Y}bϲ:<%|g5' b99حs |8`)nBVg}7s{y'Wf\[ugB^u5Cga<|Y WֹYu^,Guͯ>ZtQOlWN?]}jO7UXWKNm^$Q7{7+]\ܻ+ūwNwzrdޛ7gkl+9w>Z7nw9;~m;wvnO;w3Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:11    E(162H/G 1X+{(Mx ]EOǤ{CH0dDMJ#YhfxF QA jfyG]Yu2pB.̆XG/FH;oOn}N+U{zթsnW$W:!I#}ėP&$/Oʂ3NKd]DlW^$$?P/I䚉=IEɟ#KytXzx_)rT԰E/e v*6YPW]Mj)"~Mmw"ӾZrr*r* וrDy)x\w)hˎ;ZĒ\*<cp9z㗤}]I"YRѽI7&w ̮7gE|w_uʧ!KҾ}/Ss$˿tqd%K} n,I;o~&EmD> 7~?;"˕M-ꗞdzl;esOrr6̟%+R(mY1. 9"g]߹r$Wc9+9YJ,`xV"N^.h,u>Wo;pk4zћMcsABۿvKZ%pDE86_{׉]36Icslw>|cD06\c±*:ei$7گkL6P ߡܦޓmvBO(?!96$]UU>rGnFrɭ]:rբ \C)uɏJJ*Sɖdc¿JVQ2}腃9肃kqn(!l{Y4ˋ{зR_c4&L;[:55zmdW_ʏuv5ONܝɉs,uE|wk*sఢ+ֲutr|9ґ}EC|<+} rSœdX 7Gc'rp\ŭ_OS&ŰjF8R-+#5ȵ+GG GfÑA9e5>uO]5W &Ʒ\i9C\?L3>|o uF @F_{,/L9*;Irvuy$2Nkv~eufݿ.jkO]oy͔ެϯ<_߰e>@i1re\`sav.gn ^aʾiWGZfO130ǭ;X^!]%Q\嬕|eN;#w\ =jeh]sŠ~HXGv-2?Kݲa7Bxylռ=kk)#歱 R#݋{dkIUZZ\M^Zq}̍:R|wX9=wp.&\H>G_lg`=[{?/݋]&"i+~"?DdaM=&Ϧ(Ք[DYmSvX6<}cA#?>(!lI6\gMl{Tl{6ǖ wN0A^n~x;o:ýqqCGFĹ|A: * Frw>h>&3] )LQBñҫdF擪õ*8ØnL3]h#\n&!+`1|cYj癐Eb?e`ۯ|0M L3W}9PSYzZ)& :U|1}ޠ3V3rǤJw#K) Šxx͎1Jg576'lO3=Jmq:AY[oW>`&F6ٲ^ __A:n"}X`c5zhjƕX]D7f}WcՒPi,jAcce hyN$vX[^r1aC_>#55??}MI}MM*|ˮኀ&zy@X~ qfg v[9k@58Y"Z%ؼ^ȋyÅ !hȫ3_м^?y}&>y}U_b=| 0)6Y[7[YR/couݭ; .j]dn]8vROPO{ɇ)r>ئ6C&=/厓o^ȞޝSrSk2Y1@c]{!ehk)ñ^m+l:>' }>_u}uTD({DWѿa_֪P:LbѦ[GPb:Tٮ-J|>^#RJ,5w֢J*hme2uoWG߃rh\U嫯:v}>Q1tc|˕fk:4|ʔ9zӯi"*r}\\qc#w<ž|w tNASY4?!1)sA_"O)ۯ|eSf|[^y[N{/^Ә;īeI8+=r{Uϊqu;OѽmmGllʰe=G5!e ty6]c<wJl{F'c'13{q}!f .f7K wGG3]/or7ȡs|憴o.˅15"nJzjQ ;4|甆=п_ouH{c7gߦ"x% 0:98?S03*LmXf!n<9Gyr1<ərbc}"__A)N0a%m7aAXED\~OX[馪\[ʵm*O}v$szP9T9&ڣY}u|ǩueʈyk\܋7(\D5[iBH7ԯbd#[ЬEkΌ^ّ>Xk ۑ|<+y~7ퟩIU.t?SFl*ggNjM]#ފMU۲_.æ͍W5mutl ׿~aJʔ:}|+~\g g7KY0aVMςt`W! `VP{Nxr(Y*Pf= ec{],xj彮fx¬cixFMf0+g40+/^c%UwN~5U< \XT9MЌa`X?cPzm,%ZH KGݤ2u1C;Ct𲮦l*Otcl(ٻoNfs_)cUެ1ZڷҼ,cٷOJQ;מ1yefY" ۑ|U 5RǶ^"{a[{U~2X-"߼ªcOjJ~e?e^f O6<-o;lv p9Ҩ65>v9aÆ4w!V^2[}?;nߨZ?U ~!`?QeWOuGuXhke2c[M{ZOY䣎j>|] f6(.Y   7M_5?b|a~ic=Gݎojb Nӄ>I qD+|3Kb|av/lrwHa{'Kr?+j/F7B54=t=tJ/,B`/1~o8+} 4^b|,9?h/Velx{I^?cyi|ޯwhy?>ƾ%[yG]Z1wERoh+|wޑ{X$ٽVݬ׭J[v5Ua{qXBbo덞lg:v$k-C`$<^:W=W}T?s9- cʀo6c|+O1Dž+b| wk7;M:%_XK1~3b8 i?1~෰~X~anc|aKi- c/gRc|axO 4b|zHO\هHmgZymcg=u+{斝mE?w+1~Gi:/{8ε7(=_9~op]/,DX~|L˸[ԂYǟ@|O㷜\g4J?g 5@xx$wE .߶}Ttx 'g 0- hr+EoZ:!v v8tƷ]V|rՠj^;rm$[ov_z~bv _K9F?u;hcʵA4Z1ŞU8{SL&RU;{xZK|Ձ72i;_wBEXf7͇{/trT<СQ4x\2u4ߘ4o$+׏30ܓ/Y&Y4>D ,}J۔ Ɖ'nzIɉ1?Dq_4i V)ȵVJy=S[![>D[ԾV325gjk\.S_ן,V4(9S<1 Tek'ߓ/S"_y^4sg(۝W %6$Z)_RnYϯZ ,N^Ϳo˵EW~Fi1 xN~n˺Weg,))ǞSw3g,Gfu';\ ɦˈ(.zQFk4~)]Κk~CkW~"f'dˤUOVV:uCks*{lk5X&Zp9Aq|߃zuys^+)o@'7֊'B/_aksD;YXݯl%UzhHߥo(ߙkFW;8 {"$|޿űę54}澤'ڋCp>x8ƅNgB #y].#׮WPNnoYή4x\vFhr!Ivh\?#yz, g7#f3vTCA#>}=?ia[!_ ~]M ^6/U"a:y +q_'T.UjϞ[3O2 &l>E,˻^;WY{9c/SF}g>tbZmH课cyΩȺ]wu:Ms1y_b)h]u⩚XuyT_/EigS^2.RKj1D{\ s+5Cs6IJqU>J-A5~ ]EAuxUѾX ma[e~x4y9wռ{1Xs)#mui&j1_-+ԋs^ ՚_1yŜ\uv]'`?քKp~Ŝz9njV16gswc% ygW׶[P7D*ݪW/lP`AG#ުDً%r#}|WCzP6i̛lcq_˕VU[߆{R-KUѲP^#Ie7u2}{wmtjԞ#{ަ9r;w:ŤnixEb,07e~z4~h%̥"#0}2* /LE0s R>W#%Gz[Vtl/lGV1B94Ѫl\xs1=gtq! ?il؜x6 `罻Nm cmMmo'ccE&'2;#7bJ>x9X4uk?ɇNz:U(z3ޯ'/|eN{O-GwE.+| bm:>Xg| Q7G3ަʩ8yusk3cwX; rvz)B}rm[5(?gICjTφgVuTUoʲ5:~;R.coQ._ JV4qֱȱt쭥\cؼ~ݼ+E^ǖ(#u Rݟ}F_L&9Mztb^]6蓋5p cICcmvSb<Η>tǫm#tȑfg"oV-{Y!žbmsmGB>va'3av9)F0~Y+_aӢ,Z_Wa>*lC'Z@+[#}( ]nl=UL1m>{wƀƠqva0prIF^7 ~EsΓz8h8A'}@G"kr~#Im&WwA@ςFߐyTf~ y͠_տ,3׀ѳSv`Hs> ~% ZO'gcj^E!h+>sSqx-C 6>eA ez_M;dZ]U1;OV,opf_r 8FwYQa#d,ҠOE)2q?A̸4dZ(|S q@8rLyv~9Ik!" ӿlj6C~}VPȎ{ k Zuf[eOh֧{< PZ.esc[=>==#4۲=[C֧y@8repک$VVÑ:gU2!/|'6>WyqrΗ]I|ҞԷCH! ~78 a}Ue5Q0tNA >0k p /iHɱnH dev"b.j.PW)sQtE/`=;2Y߇ 6{NmjW *l[%F3"?o_3<@iɱ (Tg{`CO椸-SFEa!"JUO~|w3y梿1GvLJfc4ƈ7l/lGi/ew;Mm"iW pN`8Q;mvB'B=m3>|}rC|`~0tGlH;?eRurNw98~x;%ȍEA.qdsv~O; iHd{>ڼwv&zkٕGh/xϠg7yp; >ɋ?|C=m ?)WɄ=]ɋr(/[D[[i> h픎QFiLf+gGǴ^]6@W.\iM/mi$M\x!D)wPc_`tIQ[MyoPKQ2󆇈6GXVGT*w O9 <~m!j.OR}+6E-xFiod 7ʚI9h[Giv6bmϜ|Mɏ@t0y9C|1t\a]CC@<\?Lx'FWS}tvT21#yr12@M˰eܮm= mq=1)F)#hY(Et1P=itLju){!A6-V~#zE33!=` ۑ|eSfR"[i` {\xefǎsEqlSjmW۶ _-9Qyn|ne.M)T#v+ıȢe;V}?ϽmLfvz7^Fm=Nid%탷u;e2 &9eļȨ!ZLeRX%oӡKͩn~4?#iAu?ylͯ=}p;mnWEޛ--ooM՝fN^X^ D_TWK\DۑW8x9H.>p5ār`=pԉR~2^,"Z7¦;̽2F uU|g;aR\zQ5^G#{.,ȞQZbϕBK^[¨/FMǨWŨ~WQnjV1m%v`ԟj wJg1~o%NNg+ر"G9>3bWxxXgjXvx!5XviߺkV;{e`2Y2,{dwٿ1bo-SFEaK奰ߕ߻:wE<+ò,SW ϯUɎDzWu*YO1r*,ec',k*X:]#[{)޼& ;]%J˾u?sW+)F.gۉ5n&׮M\u[j^qy(æN^Zs2e-띁/wh;,"sNnFlݝmzm""mH>ުMK,6{ަMlJV;0CD!8v2x ~C L>rʱ~ǞM!XUZQBk)'Ly(󷪜ʓ>{*G~^;G.2!O-l>73ӞK[A w?<ԣRzPo? Oy= 1 #b" #sE۝~GJ|]}^ߠ4v{Q~wIq.qV1b56ӗF>hgq΋O@w% S.q;IyP?%oӸ!]jdv252zg$LG÷6Zm-WαeHi#ii#LDikzR u888-|K>tlUr}.B&kyJUZ8\Y_\?#P'O"PZq ;=?=,,!12 è ïðåäèêàò ) , , ( z y x P k , ñîîòâåòñòâóþùèé îòíîøåíèþ z y x k   . Ñèìâî- ëîì k  îáîçíà÷åíà îïåðàöèÿ äèçúþíêöèè èäåé â àëãåáðå ÷èñåë ðàçìåð- íîñòè k ( k =1,2,...). Ïðåäèêàò ) , , ( 1 z y x P k  ñîîòâåòñòâóåò îòíîøåíèþ z y x k    1 . Ñèìâîë 1   k îáîçíà÷àåò îïåðàöèþ äèçúþíêöèè èäåé â àëãåá- ðå ÷èñåë ðàçìåðíîñòè k +1. Àðãóìåíòû z y x , , ïðåäèêàòà ) , , ( z y x P k çàäàíû íà ìíîæåñòâå {0,1,..., k 2 -1}. Ïðåäèêàò 1  k P ìîæíî âûðàçèòü ÷åðåç ïðåäèêàò k P ñ ïîìîùüþ ñëåäóþùåé çàâèñèìîñòè: ). 2 , 2 , 2 ( ) 2 , , 2 ( ) 2 , 2 , ( ) , , ( ) , , ( 1 k k k k k k k k k k k k z y x P z y x P z y x P z y x P z y x P              (5.2) Ïåðâîå ñëàãàåìîå, ñòîÿùåå â ïðàâîé ÷àñòè ðàâåíñòâà (5.2), çàäàåò çíà÷åíèÿ îïåðàöèè y x z k 1    , ñîäåðæàùèåñÿ â ëåâîé âåðõíåé ÷åòâåðòè åå òàáëèöû. Âòîðîå ñëàãàåìîå çàäàåò ïðàâóþ âåðõíþþ ÷åòâåðòü òàáëè- öû. Ïîÿâëåíèå ðàçíîñòåé k y 2  è k z 2  íà ìåñòå âòîðîãî è òðåòüåãî àðãóìåíòîâ ïðåäèêàòà k P îáóñëîâëåíî òåì, ÷òî âñå çíà÷åíèÿ ïåðåìåí- íûõ y è z , ñâÿçàííûå ñ ÿ÷åéêàìè ïðàâîé âåðõíåé ÷åòâåðòè òàáëèöû, âîçðàñòàþò íà âåëè÷èíó k 2 ïî ñðàâíåíèþ ñî çíà÷åíèÿìè òåõ æå ïåðåìåííûõ äëÿ ñîîòâåòñòâóþùèõ ÿ÷ååê ëåâîé âåðõíåé ÷åòâåðòè òàáëè- öû. Òðåòüå ñëàãàåìîå çàäàåò çíà÷åíèÿ îïåðàöèè äèçúþíêöèè èäåé äëÿ íèæíåé ÷åòâåðòè òàáëèöû, à ÷åòâåðòîå – äëÿ ïðàâîé íèæíåé. Ïîÿâëå- íèå ðàçíîñòåé íà ìåñòå àðãóìåíòîâ ïðåäèêàòà k P â ýòèõ ñëàãàåìûõ îáóñëîâëåíî ðîñòîì çíà÷åíèé ñîîòâåòñòâóþùèõ ïåðåìåííûõ íà âåëè÷è- íó k 2 ïî ñðàâíåíèþ ñ èõ çíà÷åíèÿìè äëÿ ëåâîé âåðõíåé ÷åòâåðòè òàáëèöû. Íåÿâíîå çàäàíèå îïåðàöèè äèçúþíêöèè èäåé äëÿ n -ìåðíîé àëãåáðû ÷èñåë ïîëó÷àåì, âûðàæàÿ ïî ôîðìóëå (5.2) ïðåäèêàò n P ÷åðåç ïðåäèêàò 1  n P , ïðåäèêàò 1  n P – ÷åðåç ïðåäèêàò 2  k P è ò.ä. äî òåõ ïîð, ïîêà íå äîéäåò äî ïðåäèêàòà 0 P . Ïðåäèêàò æå 0 P âûðàæàåì ïî ôîðìóëå (5.1).  êà÷åñòâå ïðèìåðà íàéäåì îïèñàííûì ñïîñîáîì ôîðìóëû, çàäàþ- ùèå â íåÿâíîì âèäå îïåðàöèþ äèçúþíêöèè èäåé äëÿ îäíîìåðíîé è äâóìåðíîé àëãåáð ÷èñåë. Ïðèíèìàÿ k =0, ïî ôîðìóëàì (5.2) è (5.1) íàõîäèì: 'xlUǟsn?nb!n䇴RjT6bTfL)FTW8 % ͩm (T[ E⏉Qۍ9B-}~9S&2Zb4~"Wf!7 x8F.{GCJ]qXf{aP~#dqc adn R ;dS(뜋ɕZy^|5uȳ$Wd Y(5)_r<&KDS-vN}ْ/d}yw$ղ1'_+H|v9 dJS&n ?(Ej{rH&0>N"r˪[=G*X6c?-VswaG0ϩEY K9^ \0< &㣶Εv$3ZP~J_e^y?a=Pu]`9XIUgW A8I}jb;5;</Ǿe9\n=JHkTDVܸܮƙxgT$15xd` >s9[=7=ϟlft'k4c_(+/?s=Y̶$~SSWd){;OV|*Ԟn~%W緲獒U*O>gurnv.g=nӈKV0L*x7:+v0ط164O#55uuv3ouAk609\*_WDVu w{N+k~Zo4n`77?~V 4[ƚcϼ/Gp=0~(066=Iw 9y{3dOzZG8`#~v:kCS]9㟸~†{rְ֠y 23w/i/+p!h}_3k%ګmZ魌|Lit5bϤƯ|@*Nv&ng߹ɝw^!͕)[ԣ_d13wllVp ',so8o`|=z7 ?Jsc /zKB6J_N|i@e/wGv}C==Cӂ͏Qb󱶬޺@m~̦wIv/e{\Xw}U-R^UToB,f}e^!vX~XQ9@kg9 "rhd_Wrnyz_g^y? 5i?WMݱZ +^p)thz uL_R =8`W35=#7l,@7CBf"K@u ѩ>_qY)4:z׳oky5 `<&M<TM>1{h `kod܄Gm8>xʋHF0/X d7?'`!F}VQ ~7t/]3]O0CL+ѕo_峯|73c'Ax/cPL'Jz\lv&&G=Yo+&[Z*Iuv|Yjyk9L9W)==*2m2yc y YY+C\J70_s 4k/f"-xVAہ@;}? <%}W2NES'r~FǦgT[zG'f^2TĘz/uNozLKg&=={ *OW\{S4NW=%{|~6|}%e7|o{aco`ltAgOY6 ^;'O%&ʒڛ'{ڌibO_A \\O:K7Fad{"h39#Ke TRHe #NRHe T'Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:11  : 3(16*2*/'1wF"\y{!x \Eodp0AHH0@Tt (!H h eD+߂BB*(Qe?Y7bC@2bxD>N[ݛԽuUΩsNս]wHe^74~Ln,;U$c,+LzY6$]l,ۊ턙%$ܲM=KсlEK69;7;3;;;?+gQve|[; \ >tpNUu g)m@h?dt;ۍф^BQеR#Hxtqz!ݢAmٰaCQ:WkJ3lfHt"Gz ;d"mH9ikmu.7/Fd?֥ڳkkat';jOl}.;kgfvd}#fsI/lG옑djO~rt nWVeG?}/`ON<{n_:=K-oa:@{;{ʮb,ڒ>,o.>C [#6|xCЖXdj$퟽X,%y;I\[Uj)lnAz ٤&2csٜ 7e䲩 ^lĒMCSs[^dSen&H6+#T,T,KlW^6Sӽ<﷧LɆ虾t(\5V,]#nɲUo]&ݟ:TOw*T)_wnJRusË~Ԗ_e˱iVvU򲖡_M/ CLY-ShzfY)jLh.j&\|*{y{ MFtU2]b&tkBh:{gl-)<{+J}ďe/|"4x\Ü-U}JA*Y@u/tO;LnB~g'׸y~J׊u-zw5zʯ|]~ AfGEjNk#Jӹ" `dEOCS]%!enɹ g%ΏoOW~v^*>;/g}îXޫO%i&AzLny=k5ܠ9՘wm}f\6ŞLC YPį10?y->ޭo~|Z}GwzMklűse8VBZu3}pWⱄj>)_ _V83t w@!z(%t9JZ'i XxcK!?{2c ٓ)x1B >lceȶ[ide_XiUJV~'| ʉD+;o骛 C?(*?\Og /^T{LsdKm0s.Om}'/w 6I#4$H7!}9\hDK4xF\_+T|QUKҠgw}R% ?cWlmEC/^kTAjyWVO UYnQ1~I7tG^cuU/܋pzfasq Zh]А)8Y%H g{Cjd-nFbO©8n=K-ܛ {V0wd.i{*-b -ܛ/(nZ>씖wV-ܷS~ z BN]8-Ə;OMl/%z;/m=4a$)8eu6_Ty=*Wrkk@ s\fu3iùՄ H~mM>Ҵ>)F޿5槕k kZSX׌5[o/)ǚޭQz))<$^Uy ןc8c:Ψ@r(/B3y.kk ~6URk99*(],=S jM}^ܳP⫞I=KxlڞTpClqsSj~1<)Ǻ)qXm5 ץGZkWɅsN79/eNYL&S攕|F)_4?tQkN)9RWݺ'[}]띦'ˏ_,Kyn7H!`"҂Fep+靝Bc܏j1ߴCN-)]Lu.~7y75Njp^^x~wvsFoBU^k?6(lvWud(Mle_UG=(J{ѨFOlT{<z{;[A1{9ahͶWd)0dgy&}}uwh pӟ=a7ﷁf|}{pٞd/Ꮷ%OI~@p0}3~ At ?ڻoƯiRqzEï\|l.&9+_4?.̕k#!y_=˪C/惟@bow t;n#Tmxh-#o S6{bڻo/TCAmqXOW;R*^Xw@i|wuܨ_^V{u*y}34p7Uv58}ݷzuʃh~ߕצw?0ڸݛZ[DPyzw*|^?i$j_焾0{o`wΧ:ȏ}>𶇛곌ݸg7i=EYƽsG-O|_@SڞZc^rޯ{ե)YVU5]<}gU)Z+ _Q^i}Qӽ~еK*W_Xxbר utMe*Fs(kV:9ҔOe׹ ':';UJM!E^Uxy i%dk)v x#+IH,4qWtz83OGj"c+K)J]M[4x>ӹZA}|Z})ҭl*Vy|[~)M[lK֞F+ij? &_ {><Ɨ&O!Su-YRb搜Gq+4Q\w{5%Q󶾞ܓ޵e&A6w !>?}D]}NF=wUG1<}+&7E8dHcڼ5oQ5YB3ehuZ{ '>ӅSoLC:Q)P)(76Y;D8ߎsqtRpcRp0o""啂-pwG cڠX\GI}'L{ߺWMs}o)o&O0"y-aEy1760"YtgP'ygӽq #ש>)TBeȇsJBCN1D=s{X-de~{Q/1IeE%M.*yys$zgC7\Ȯ l-IO'=o'}gϟov_>lx Z@!Ai{ :4W_ZY*Wt(|v_*WVMuڵӵq}ǪRƀxR㭄Oë)ME~ډsݗ?X+]iw)}}3]ҬLNUɼ] kNeZF1GMV[~YGQ_#~ _uS|K7Sl m[ _.qh/{V76c i4@=ŷᅠ{#y^Pt<ݷ30"%M9ttF#;|{`|D8O<ݻХUވGyb#{;:yopittW Qyd4yף#{st*yj<{sRypn5p sToA!Ա?ypn=|{g#]s>r9HOpc#=RtoAD8OW>'y/pgg<_G8Ow/c|G8O#p1{(MXٵ{$km@]la]G ߧVʞ֪{Z_8c+[^ƺ:(pjjhy:WSp))sk)T<ׅ*+k77 )_=hAyTwۃ~IDRpF?F8]a"K>M,7pwYq'VU|vN|"F8Oi!)݁|D#[Rpq؁QVGoD8_[=E8_X_H-e%7 E8_(6yvb?~+E8_swJtc$y#)3} u 9<Ϫ/)\ pDoD8_푫|<$/ybG8_=U >/yD^}o3g^T״cT^${tεofoF_%e b4IK_{hgMءPYyi ic}c㎒K.@WPiFj,w5oE1.Q? _ s.VGu2++\ ÒNN[,e=˯t˫1N:ZQl4S{iog"V|?.= M_B|ηsDerPKt{} 4=";} o=@f#\;x{6q%ck,[KVumqn"_#] b |FLxr(4n5y6I#*V>wa9y)%4i9ExJTym6K|"HTY$tPTYKbwiK٬;I|K/WNR}eV`t] ; >JGA'Ɏi9&/KN%<ɿlj<,lts'2 9FvAז.u_Xl .oV>3kAtT¨JW#oe(U/atU)/O_E!O%+[MZe[}^ސB@w%}!NcOUq;dcPJc~L%Tpc߫} O/NQekϊ5eڗǺ=(s)Ѳz(ªP,T_+_B4R[Q>P^*C+11<+Ci_ x_>c99x~M72Xgt][lӣ!=_O[9o&w+>?&3&B9@C~wJݧ|qXQP߶9_f<$uOrcRWW9/g#o۵s$+7p}d#*n&A^ryU>=Qkk`|fɈ>_`m뫿?nD)d"6_97~+ع۰V}\KVUc*C¹0T/b1%zYQF%Y:ߐ #F["NGoKHT| ɗ}Vq.Z j{YObɫSiWڴC=ow4Tn smbϫwaw\k%sWr Xy5,l8jtHk_>?]ؓt.й|!Q]u.K:|%C*ª?}_YB ^۱5wu l3е:~˷'=0 8_{L{#j5GC1뚃GͲƯɎ_|4wο5{/iKϓ>XPG6冢/1jU/lUr ?|c5k论ߵ4=-l9YfG*Sm TBe@\iwuOvWXl 5R>IJQK$Ms^ Uk_iv\O0=q\=[-ǏV#-e[Xܯ>ڑit!ZNX3rlԞ\踾Ub+2W}adww9Q=K-oa:@{;{ʮb,ڒjkT+d)(G٧9qNNe| bIst[yAƨCYF^vCdQ6~ɋUeqhlY/A:kO% GYu9_|,ҁrzeyv׵_!mYsg7p駟酉YatX 062_Κ8n:gYpmuUXu QiGvzU+TʢꤞT",'O? eC?5!4eof[V??˺C>,KEZA lΨ6ڪ;~|t:ȣ:tw^PqگCvGoO-گ^Zk6(rdVk!b/ő J<5َp ya8x+ٯJl5eeuB뭅Lk*دn~ 3AFG#jޓ1Wvد44~Z4Mh1n:hn>lO-xD\i?%#H,,[13 . ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 2 , 2 , 2 ( ) 2 , , 2 ( ) 2 , 2 , ( ) , , ( ) , , ( 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1                        z y x z y x z y x z y x z y x P z y x P z y x P z y x P z y x P  àëãåáðå êîíå÷íûõ ïðåäèêàòîâ ïðè ëþáûõ íàòóðàëüíûõ çíà÷åíèÿõ b a x , , èìååò ìåñòî ñëåäóþùåå ðàâåíñòâî: b a b x a x    ) ( . (5.3) Äåéñòâèòåëüíî, åñëè 1 ) (   b a x , òî b a x   , b a x   , 1   b a x ; åñëè æå 0 ) (   b a x , òî b a x   , b a x   , 0   b a x . Ïîëüçóÿñü çàâèñèìîñòüþ (5.3), ïîëó÷àåì îêîí÷àòåëüíîå âûðàæåíèå, çàäàþùåå â íåÿâíîì âèäå îïåðàöèþ äèçúþíêöèè èäåé äëÿ îäíîìåðíîé àëãåáðû ÷èñåë: . ) , , ( 1 1 1 1 0 1 1 1 0 0 0 0 1 z y x z y x z y x z y x z y x P     Èñïîëüçóÿ òîëüêî ÷òî ïîëó÷åííóþ ôîðìóëó äëÿ ïðåäèêàòà 1 P , ñ ïîìîùüþ ðàâåíñòâ (5.2) è (5.3) íàõîäèì íåÿâíîå çàäàíèå îïåðàöèè äèçúþíêöèè èäåé äëÿ äâóìåðíîé àëãåáðû ÷èñåë: . ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 ( ) 2 , 2 , 2 ( ) 2 , , 2 ( ) 2 , 2 , ( ) , , ( ) , , ( 3 3 3 3 2 3 3 3 2 2 2 2 3 1 3 3 0 3 3 1 2 2 0 2 3 3 1 3 2 1 3 3 0 2 2 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 2 z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x z y x P z y x P z y x P z y x P z y x P                                                                           Ïîíÿòèå àëãåáðû èäåé ðàíåå áûëî îïðåäåëåíî äëÿ ðàçìåðíîñòåé n =1,2.... Ñëó÷àé íóëåâîé ðàçìåðíîñòè, êàê âûðîæäåííûé, íå ðàññìàò- ðèâàëñÿ. Îäíàêî ïðè ìàòåìàòè÷åñêîì îïèñàíèè îïåðàöèè äèçúþíêöèè èäåé â àëãåáðå ÷èñåë, ÿâëÿþùåéñÿ îäíèì èç âàðèàíòîâ àëãåáðû èäåé, íàì ïðèøëîñü ââåñòè íèêàê íå èíòåðïðåòèðóåìûé ïðåäèêàò 0 P . 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Ëþáàÿ äâóìåñòíàÿ îïåðàöèÿ, çàäàííàÿ íà äâóõýëåìåíòíîì ìíîæåñòâå 1 S ={0, 1}, ïîëíîñòüþ îïðåäå- ëÿåòñÿ àêñèîìàìè èäåìïîòåíòíîñòè, êîììóòàòèâíîñòè è íóëÿ. Äåéñòâè- òåëüíî, ïî àêñèîìå íóëÿ íàõîäèì 0  0=0, 0  1=1. Èç àêñèîìû êîììó- òàòèâíîñòè ñëåäóåò 1  0=0  1=1. Àêñèîìà æå èäåìïîòåíòíîñòè äàåò 1  1=1. Ìû ïðèøëè ê îïåðàöèè äèçúþíêöèè äâîè÷íûõ çíàêîâ, êîòî- ðàÿ êàê èçâåñòíî, àññîöèàòèâíà. Àêñèîìà îäíîìåðíîñòè, î÷åâèäíî, òàêæå âûïîëíÿåòñÿ. Òàêèì îáðàçîì, ïðè n =1 àêñèîìû àññîöèàòèâíîñ- òè è îäíîìåðíîñòè ëîãè÷åñêè âûâîäèìû èç îñòàëüíûõ àêñèîì, ôèãóðè- ðóþùèõ â îïðåäåëåíèè ïîíÿòèÿ àëãåáðû èäåé ïðîèçâîëüíîé ðàçìåðíî- ñòè. Ñëåäîâàòåëüíî, ýòè äâå àêñèîìû ìîæíî èñêëþ÷èòü èç îïðåäåëåíèÿ îäíîìåðíîé àëãåáðû èäåé. Ìû ïðèõîäèì ê ñëåäóþùåìó îïðåäåëåíèþ. Îäíîìåðíîé àëãåáðîé èäåé íàçûâàåì ëþáóþ àëãåáðàè÷åñêóþ ñèñòåìó, ñîñòîÿùóþ èç äâóõýëåìåíòíîãî ìíîæåñòâà 1 S , îòíîøåíèÿ ðàâåíñòâà y x  è îïåðàöèè y x  ( 1 , , S y x y x   ), åñëè äëÿ íåå ïðè ëþáîì 1 S x  х х x   , х х   0 è ïðè ëþáûõ 1 , S y x  . х у y x    Îêàçûâàåòñÿ, ÷òî àêñèîìû èäåìïîòåíòíîñòè, êîììóòàòèâíîñòè è íóëÿ, ôèãóðèðóþùèå â òîëüêî ÷òî ñôîðìóëèðîâàííîì îïðåäåëåíèè, ëîãè÷åñêè íå çàâèñÿò äðóã îò äðóãà. Äîêàæåì ýòî. Ïðèíèìàåì 1 S ={0, 1}. Îïðåäåëèì îïåðàöèþ äèçúþíêöèè èäåé êàê íåðàâíîçíà÷íîñòü äâî- è÷íûõ çíàêîâ у х y x    . Òàêàÿ îïåðàöèÿ íå óäîâëåòâîðÿåò àêñèîìå èäåìïîòåíòíîñòè (1  1=0), íî ïîä÷èíÿåòñÿ àêñèîìå êîììóòàòèâíîñòè ( х у у х    ) è àêñèîìå íóëÿ ( х х   0 ). Äàëåå, îïðåäåëÿÿ îïåðàöèþ äèçúþíêöèè èäåé êàê ôóíêöèþ у y x   , âèäèì, ÷òî îíà íåêîììóòà- òèâíà (0  1=1, 1  0=0), íî èäåìïîòåíòíà ( х х x   ) è óäîâëåòâîðÿåò àêñèîìå íóëÿ ( у y   0 ). Íàêîíåö, ïðèíèìàÿ â ðîëè îïåðàöèè äèçú- þíêöèè èäåé êîíúíêöèþ äâîè÷íûõ çíàêîâ ху y x   , íàõîäèì, ÷òî îíà èäåìïîòåíòíà ( х xх  ) è êîììóòàòèâíà ( ух ху  ), íî íå ïîä÷èíÿåò- ñÿ àêñèîìå íóëÿ ( 0 1 0   ). Èòàê, ìû äîêàçàëè íåçàâèñèìîñòü àêñèîì èäåìïîòåíòíîñòè, êîììóòàòèâíîñòè è íóëÿ äðóã îò äðóãà. Ïîýòîìó íè îäíà èç ýòèõ àêñèîì íå ìîæåò áûòü èñêëþ÷åíà èç ïðèâåäåííîãî âûøå îïðåäåëåíèÿ îäíîìåðíîé àëãåáðû èäåé.  äâóìåðíîì ñëó÷àå íè îäíó èç ïÿòè àêñèîì íåâîçìîæíî èñêëþ- ÷èòü èç îïðåäåëåíèÿ àëãåáðû èäåé. Íåëüçÿ îáîéòèñü â îïðåäåëåíèè äâóìåðíîé àëãåáðû èäåé è áåç òðåáîâàíèÿ ÷åòûðåõýëåìåíòíîñòè ìíî- æåñòâà 2 S . Äîêàæåì ýòî. Äëÿ äîêàçàòåëüñòâà íåçàâèñèìîñòè àêñèîìû àññîöèàòèâíîñòè îïðåäåëèì îïåðàöèþ äèçúþíêöèè èäåé òàáë. 5.2. 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Zܿι* ?,ɯ?^ͯB y3WЭ+/G XI )Mvm79oTgߵQ~ӵ6z󛼟&ͺ|džh5۶p՟=zm_6/+^#snP^^}Zr#YT߫UǂіN|nFAF\F,, 17 èç íåå ìîæíî èñêëþ÷èòü òðåáîâàíèå ïîïàðíîãî ðàçëè÷èÿ îáðàçóþùèõ èäåé 0, . ,..., , 2 1 n e e e Äåëî â òîì, ÷òî, ñîãëàñíî òåîðåìå î ñòàíäàðòíîé ôîðìå, ÷èñëî âñåõ èäåé â ìíîæåñòâå n S íå ìîæåò ïðåâûñèòü âåëè÷èíû t 2 , ãäå t – ÷èñëî âñåõ ðàçëè÷íûõ íåíóëåâûõ áàçèñíûõ èäåé. Åñëè áû íåêîòîðûå èç áàçèñíûõ èäåé, ôèãóðèðóþùèõ â îïðåäåëåíèè n -ìåðíîé àëãåáðû èäåé, ñîâïàëè äðóã ñ äðóãîì èëè ñ íóëåì, òî îêàçàëîñü áû, ÷òî n t  . Íî ýòîò âûâîä ïðîòèâîðå÷èò òðåáîâàíèþ n 2 -ýëåìåíòíîñòè ìíî- æåñòâà n S . Òàêèì îáðàçîì, óñëîâèå ïîïàðíîãî ðàçëè÷èÿ îáðàçóþùèõ èäåé âûòåêàåò èç ñîâîêóïíîñòè âñåõ îñòàëüíûõ ñâîéñòâ, ïðèñóòñòâóþ- ùèõ â îïðåäåëåíèè n -ìåðíîé àëãåáðû èäåé. Ñ ó÷åòîì ñêàçàííîãî àêñèîìà n -ìåðíîñòè ìîæåò áûòü çàïèñàíà â ñëåäóþùåé áîëåå ïðîñòîé ôîðìóëèðîâêå: ”  ìíîæåñòâå n S ñîäåðæàòñÿ òàêèå ýëåìåíòû n e e e ,..., , 2 1 , ÷òî èç íèõ è èç ýëåìåíòà 0 ìîæíî ñ ïîìîùüþ îïåðàöèè  ïîëó÷èòü ëþáîé ýëåìåíò ìíîæåñòâà n S “ . Îïèøåì íà ÿçûêå àëãåáðû êîíå÷íûõ ïðåäèêàòîâ â ôîðìå íåÿâíîãî çàäàíèÿ îïåðàöèþ k -çíà÷íîé äèçúþíêöèè ( k =1,2,...). Ñ ýòîé öåëüþ ââåäåì ïðåäèêàò ) ( x Q k , çàäàþùèé îáëàñòü îïðåäåëåíèÿ k -çíà÷íûõ ïåðåìåííûõ {0,1,..., k -1}. Ïðåäèêàò 1  k Q âûðàæàåòñÿ ÷åðåç ïðåäèêàò k Q ñëåäóþùèì îáðàçîì: k x x Q x Q k k     ) ( ) ( 1 . (5.4) Ïîëàãàåì, ÷òî 0 1 ) ( x x Q  . (5.5) Ââåäåì, êðîìå òîãî, ïðåäèêàò ) , , ( z y x R k , ñîîòâåòñòâóþùèé îòíîøå- íèþ z y x k   . Ñèìâîë k  îáîçíà÷àåò îïåðàöèþ k -çíà÷íîé äèçúþíê- öèè: ). , max( y x y x k   Ïðåäèêàò 1  k R âûðàæàåòñÿ ÷åðåç ïðåäèêàò k R ñëåäóþùèì îáðàçîì: . ) ( ) ( ) , , ( ) , , ( 1 1 1 k k k k k k k k z y Q x z y x Q z y x R z y x R       (5.6) Ïîëàãàåì, ÷òî 0 0 0 1 ) , , ( z y x z y x R  . (5.7) P"xlǿ[mi]˄f^StѰ3Lb##Hz`DAZ&JQʨ26uq_|s%&ߞ<eDbo#&zݣ+샔WOqfY gsfӻ9܉30ESG'4Gg},l?9tW;}mWsR:H\&?DnMtӫr [m ?cp.H0owl/+k5űYN̺l>~rqb\L}9Ûb]r6kθоv^\n;F|mOn_|o~SykZ'cys9ydNX#Ali`4NF@7ؤ!o7ۢ[vy?کXʗ2-?(vw Fm j8=crr7(2ZDN;A -C[KO0~jk{0O{skB.X{Ҫ{RK9V>Ryo;oC&Uz3x> ʾcoRb_}f}kQr~Z֨-XS9(?nt!X&(^]ЋK}+3{3r-x8"&.1j'`~xs6hd<;{ĶK8荒s96Yϸ} HA2{uYߏ>{St6|y;A[%m0G@Sw57f_0k߯޾%d9GNgn%0 [oC֮ad㛈__Y̍ 9קA6GdU^^˕Ff9IB')ըXCAysfpR]/p$}3n^GH==r]Oⳅm NsOۜ>9TeԟS:CDKsA~IvfJ򌇗cޥ/2 ~o{ @n& \4. 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Òîãäà ïàðà ( y x, ) ïðèíàäëåæèò îòíîøåíèþ  â òîì è òîëüêî òîì ñëó÷àå, åñëè { p i i i e e e ,..., , 2 1 }  { q j j j e e e ,..., , 2 1 }. Ïðàâèëî îçíà÷àåò, ÷òî ïðè  x 0 è  y 0 ëþáàÿ ïàðà ( y x, ) ïðèíàäëåæèò îòíîøåíèþ  â òîì è òîëüêî òîì ñëó÷àå, êîãäà âñå áàçèñíûå ñèìâîëû, âõîäÿùèå â ñîñòàâ èäåè x , âõîäÿò òàêæå è â ñîñòàâ èäåè y . Ñïðàâåäëèâîñòü òðåòüåãî ïðàâèëà ìîæíî ïðîäåìîíñòðèðîâàòü íà ìàòåðèàëå òîëüêî ÷òî ðàññìîòðåííîãî ïðèìåðà. Òàê, 3 1 e e  3 2 1 e e e , íî 3 2 e e < 3 1 e e , âìåñòå ñ òåì { 3 1 e e }  { 3 2 1 e e e }, íî { 3 2 e e } { 3 1 e e }. Äëÿ äîêàçàòåëüñòâà òðåòüåãî ïðàâèëà äîñòàòî÷íî óñòàíîâèòü, ÷òî: à) îíî âûïîëíÿåòñÿ â àëãåáðå 1 L , á) èç ïðåäïîëîæåíèÿ, ÷òî òðåòüå ïðàâèëî âûïîëíÿåòñÿ â àëãåáðå 1  k L , âûòåêàåò åãî âûïîëíåíèå òàêæå è â àëãåáðå k L .  àëãåáðå 1 L èìååòñÿ âñåãî ëèøü îäíà ïàðà ( 1 e , 2 e ) íåíóëåâûõ èäåé. Ïîñêîëüêó 1 1 1 e e e   , òî 1 1 e e  . Âìåñòå ñ òåì, { 1 e }  { 1 e }. Òàêèì îáðàçîì, òðåòüå ïðàâèëî â àëãåáðå 1 L âûïîëíÿåòñÿ. Ïðåäïîëîæèì, ÷òî â àëãåáðå 1  k L òðåòüå ïðàâèëî âûïîëíÿåòñÿ. Ýòî îçíà÷àåò, ÷òî äëÿ ëþáûõ p i i i e e e x ... 2 1  è q j j j e e e у ... 2 1  ( 1 ,   k S y x ) óñëîâèå { p i i i e e e ... 2 1 }  { q j j j e e e ... 2 1 } ðàâíîñèëüíî óòâåðæäåíèþ y x  . ×òîáû äîêàçàòü âûïîëíåíèå òðåòüåãî ïðàâèëà â àëãåáðå k L , äîñòàòî÷íî ïðîâåðèòü åãî ñïðàâåäëèâîñòü äëÿ ïàð âèäà ( y x, ), ( k e , k e ), ( x , k e ), ( k e , x ), ( k e , k xe ), ( k xe , k e ), ( x , k ye ), ( k xe , y ), ( k xe , k ye ). Çäåñü èìå- åòñÿ â âèäó, ÷òî x , y – ïðîèçâîëüíûå íåíóëåâûå èäåè, ïðèíàäëåæà- ùèå ìíîæåñòâó 1  k S . Äëÿ ïàðû ( y x, ) òðåòüå ïðàâèëî âûïîëíÿåòñÿ ïî èíäóêòèâíîìó ïðåäïîëîæåíèþ. Ïàðà ( k e , k e ) ïðèíàäëåæèò îòíîøåíèþ  , ïîñêîëüêó k k k e e e   . Âìåñòå ñ òåì, { k e }  { k e }. Ïàðû ( x , k e ) è ( k e , x ) íå ïðèíàäëåæàò îòíîøåíèþ  , ïîñêîëüêó k e x  = x e k  = k xe è k k xe e  , k k xe х  . Âìåñòå ñ òåì, { p i i i e e e ... 2 1 } { k e } è { k e } { p i i i e e e ... 2 1 }. Ïàðà ( k e , k xe ) ïðèíàäëåæèò îòíîøåíèþ  , à ïàðà ( k xe , k e ) – íåò, ïîñêîëü- êó k k xe e  = k k e xe  = k xe è k k xe e  . 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GaIa㳞ђsrڽQ o^Ȼs>0_ >0!g^x ayγe鼠sϝ6/xG owߨ(HSzu؛٪# -*KR2i`NC5t47&>یŭϑWcx:kzkg:ŽP](#nheA! j9XWMn#m㝾?􏶺ϖÇi|b7>iA3Bi!<=nINTEq7ɟ8/%aؙW?Q/a_C07'<$']!xcdxf?U<<8k{^ 㴛rk-5E`;p~g8uE)ɛ՗d\.ď_S?X:?Y?[tڻCz G!]t)6fkN"I94ho7V#,m^[ă'Z FAMC5 22Mw̭5_>uI۝$q\\-!3?NAMLam\})}l&IMtYuL.|,33ٳ|,+ #v1EfFCnylcA'ݲwQ99axrSjzgǚC@kQHA61]JM+D)z2'5ikۙL.P'ebǛƾ[2#kiv^|~ԫN4vȦ?KɰiD\x)bƒVnVYȻ^\e]uj̓D0uf).KJi=M;~~/yMs BH ~,?]B7mw,nsYg˱}xl:agQ;ҐݹӔ<8"l,&?P?H;x/\&H]T9@qBF@I!# v)r2;{7?Zaͷ) /Cyg~L:ټo usZY!b ?;8P,,21 k e }, à { p i i i e e e ... 2 1 , k e } { k e }. Ïàðà ( k xe , у ) íå ïðèíàäëåæèò îòíîøå- íèþ  , ïîñêîëüêó у xe k  = . ) ( у e у x k   Âìåñòå ñ òåì, { p i i i e e e ... 2 1 , k e }  { q j j j e e e ... 2 1 }. Åñëè y x  , òî у у x   , è òîãäà ïàðû ( x , k ye ), ( k xe , k ye ) ïðèíàä- ëåæàò îòíîøåíèþ  , ïîñêîëüêó k k ye e  = , ) ( k k уe e у x   k k ye xe  = . ) ( k k уe e у x   Âìåñòå ñ òåì, { p i i i e e e ... 2 1 }  { q j j j e e e ... 2 1 }, îò- êóäà { p i i i e e e ... 2 1 , k e }  { q j j j e e e ... 2 1 , k e }, { p i i i e e e ... 2 1 , k e }  { q j j j e e e ... 2 1 , k e }. Åñëè æå х у , òî у у x   è òîãäà ïàðû ( x , k ye ), ( k xe , k ye ) íå ïðèíàäëåæàò îòíîøåíèþ  , ïîñêîëüêó k ye x  = , ) ( k k уe e у x   k k ye xe  = , ) ( k k уe e у x   . Âìåñòå ñ òåì, { p i i i e e e ... 2 1 } { q j j j e e e ... 2 1 }, îòêóäà { p i i i e e e ... 2 1 } { q j j j e e e ... 2 1 , k e }, { p i i i e e e ... 2 1 , k e } { q j j j e e e ... 2 1 , k e }. Èòàê, ñïðàâåäëèâîñòü òðåòüåãî ïðàâèëà äîêàçàíà. Îïèñàííûå âûøå ïðàâèëà, ïî êîòîðûì ìîæíî îïðåäåëèòü, âûïîë- íÿåòñÿ èëè íåò îòíîøåíèå y x  äëÿ ïðîèçâîëüíûõ èäåé x è y , ëåãêî ïåðåâîäÿòñÿ ñ ÿçûêà êàíîíè÷åñêîé àëãåáðû èäåé íà ÿçûê ôîðìóë ïðîèçâîëüíîé àëãåáðû èäåé. Áóäåì ãîâîðèòü, ÷òî íóëåâàÿ ñòàíäàðòíàÿ ôîðìà ÿâëÿåòñÿ ÷àñòüþ ëþáîé ñòàíäàðòíîé ôîðìû. Áóäåì, êðîìå òîãî, ñ÷èòàòü, ÷òî íåíóëåâàÿ ñòàíäàðòíàÿ ôîðìà p i i i e e e f     ... 2 1 ( 1  p ) ÿâëÿåòñÿ ÷àñòüþ íåíóëåâîé ñòàíäàðòíîé ôîðìû q j j j e e e g     ... 2 1 ( 1  g ), åñëè âñå áàçèñíûå ñèìâîëû, âõîäÿùèå â ñîñòàâ ñòàíäàðòíîé ôîðìû f , âõîäÿò òàêæå â ñîñòàâ ñòàíäàðòíîé ôîðìû g , èíà÷å ãîâîðÿ, åñëè { p i i i e e e ... 2 1 }  { q j j j e e e ... 2 1 }. Òîãäà îòíîøåíèå y x  áóäåò âûïîë- íÿòüñÿ â òîì è òîëüêî â òîì ñëó÷àå, êîãäà ñòàíäàðòíàÿ ôîðìà èäåè x ÿâëÿåòñÿ ÷àñòüþ ñòàíäàðòíîé ôîðìû èäåè y . Íàïðèìåð, åñëè 3 1 e e x   è 4 3 2 1 e e e e y     , òî y x  , åñëè æå 4 2 e e x   è 4 3 1 e e e y    , òî х у . Åñëè y x  , òî áóäåì ãîâîðèòü, ÷òî èäåÿ x ìåíüøå èëè ðàâíà èäåå y . Åñëè y x  è y x  , òî áóäåì ïèñàòü y x  è ãîâîðèòü, ÷òî x ìåíüøå y . Ñòàíäàðòíóþ ôîðìó f áóäåì íàçûâàòü ñîáñòâåííîé ÷àñòüþ ñòàíäàðò- íîé ôîðìû g , åñëè f ÿâëÿåòñÿ ÷àñòüþ g è, êðîìå òîãî, f è g íå ñîâïàäàþò äðóã ñ äðóãîì. 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Íàïðèìåð, åñëè 2 1 e e x   è 4 2 1 e e e y    , òî y x  , åñëè æå 3 2 e e x   , 3 2 e e y   , òî х у . Îïèøåì íà ÿçûêå àëãåáðû êîíå÷íûõ ïðåäèêàòîâ â ôîðìå íåÿâíîãî çàäàíèÿ îòíîøåíèå  n -ìåðíîé àëãåáðû ÷èñåë. Ñ ýòîé öåëüþ ââåäåì ïðåäèêàò ) , ( y x T k , ñîîòâåòñòâóþùèé îòíîøåíèþ y x k  . Ñèìâîëîì k  îáîçíà÷åíî îòíîøåíèå “ ìåíüøå èëè ðàâíî ” â àëãåáðå ÷èñåë ðàçìåðíîñ- òè k ( k =0, 1, 2, ..). Àðãóìåíòû x , y ïðåäèêàòà ) , ( y x T k çàäàíû íà ìíîæåñòâå {0, 1, .., k 2 -1}. Ïîñêîëüêó ñîîòíîøåíèÿ y x  è y y x   ðàâíîñèëüíû, òî ïðè ëþáûõ k S y x  , ). , , ( ) , ( y y x P y x T k k  (5.8) Èç ðàâåíñòâ (5.1) è (5.8) âûâîäèì: . ) , ( 0 0 0 y x y x T  (5.9) Èç ðàâåíñòâ (5.2) è (5.8) ïîëó÷àåì: ) , ( 1 y x T k  = ) , , ( 1 y y x P k  =  ) , , ( y y x P k     ) 2 , 2 , ( k k k y y x P    ) 2 , , 2 ( k k k y y x P ). 2 , 2 , 2 ( k k k k y y x P     ×èñëà y è k y 2  íèêîãäà âìåñòå íå ïðèíàäëåæàò ìíîæåñòâó k S , ïîýòîìó ïðè ëþáîì çíà÷åíèè ïåðåìåííîé y . 0 ) 2 , , 2 (    k k k y y x P Ñêàçàííîå ïðèâîäèò ê ñëåäóþùåìó îêîí÷àòåëüíîìó âûðàæåíèþ äëÿ ïðåäèêàòà 1  k T : ). 2 , 2 ( ) 2 , ( ) , ( ) , ( 1 k k k k k k k y x T y x T y x T y x T         (5.10)  êà÷åñòâå ïðèìåðà íàéäåì ñ ïîìîùüþ çàâèñèìîñòåé (5.9) è (5.10) ôîðìóëû, çàäàþùèå îòíîøåíèå y x  äëÿ îäíîìåðíîé è äâóìåðíîé àëãåáð ÷èñåë. Ïðèíèìàÿ k = 0, íàõîäèì ) , ( 1 y x T =  ) , ( 0 y x T   ) 2 , ( 0 0 y x T ) 2 , 2 ( 0 0 0   y x T = . ) 1 ( ) 1 ( ) 1 ( 0 0 0 0 0       y x y x y x Ïîëüçóÿñü çàâèñèìîñòüþ (5.3), ïîëó÷àåì îêîí÷àòåëüíîå âûðàæåíèå, çàäàþùåå â íåÿâíîì âèäå îòíîøåíèå y x  â îäíîìåðíîé àëãåáðå ÷èñåë: W.xlǟo[ZH׎cfXdȰNffHY܆"j!(U:B-s Q~tfLV52Yf}y{}{[6\ror<߆D"R0LKȱ!WREfeg 'r{F~3RTfƖdžV]jhKZlC7Rǣ \IR=&#%]#7JDw#͕;d<Z.Ýy}y g鎔7Ыq=.,g=R 7Hycٌfs Y9C4NqkWDkT|IGSj&7SݰLBw^-=n<(Ona籼Ğ(ݒAloga8VY<+NK'r\78E-re, blϋԷ[2ԩs1]jFc[7]gzLr3.egG9<}1Vcg:{tlbtWMW`r`}z>lpP V2e,`z s{=8>yzQ˷Mo`m;B F{2OOV] Ji, F!`K"i'LF6aS(ZdL⏒yamfewRW=SwaT2`#3Qy?ɩaP]X~;JBZl2}3ZZ$rb%"dr|yϺOc#/1.*m0ኤ`ᖣkyzz_ayF_m^3_WÍ(T?Cpxa^sPjjl3T;k{1W :N6t-@^Fw4GK܅5ϛȏ%xKYہ9/0*s[wzG y[]OSor:#,Ědg^عAS7c"sG{_R7K8r'_{Jr=>`vΎVk<ϯ\ڻ\~/.w|FY-#WcgMH}\zja#sy40EYC/ωO Y̮_NQEVhk'=N?/Ow(|=?wiuqAK<^9B?j׃\C<._xvpև_&i|ge[r[O<ȧjп}]mMrv?xJkյ$w(wkKn:V&?I$H"D@":D @kMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:17  p4 ,E`h(1602f/ v1 Zi{Px U}Ĝ1BzxHxG;;+gflfrNf=fZZoך(KEسUDyfMwN9ףh Ze Wex;_>'^}OCڑm裞QK]ke͌UWs_r*L=Bwһ/w!')jKѴrr-9]-”sv㚫+|wHl߾=j=u[jG?$cp]MZ&_Ӻ^gߡeGW̜on3^ŗEѾ9hp140yH9cZs^7,V~htPq呺K_OGm6T}9#=p-qtw9 s܉D7_^d]wY[uxG><WM|M;Ҙ> +Y״el4R8?~+/}I[4E /ʵTGF^ ՗º*˪߶Ê_%<?U&E7 7/g$ໜoh?~&>}?oBo*eh?_e7?Nm0O:cG*4R;j>髕\uVTgη5UQ.}(=e3Τ '+.x}?>]?2dwE>ЊOsrIYC =2[~~t]P1*wCj ݽ!:=:%zr#4һΑ<#RY c=qK>6}-G ˴e\n%Mk|*h͒y/^p;߷ ׼|ޠ^6ro_m]SߨSo /GO|Q&}Rt߀_Y>oH~t?9BQ! 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Ñîãëàñíî çàêîíó íóëÿ äëÿ ëþáîãî n S x  x x   0 , ñëåäîâàòåëüíî, x  0 . Òàêèì îáðàçîì, èäåÿ 0 â ìíîæåñòâå n S – íàèìåíüøàÿ .  ëþáîé àëãåáðå èäåé n L ïðè n =1, 2,... ìîæíî ââåñòè åäèíè÷íóþ èäåþ èëè åäèíèöó, îáîçíà÷àåìóþ ñèìâîëîì 1, ñòàíäàðòíàÿ ôîðìà êîòîðîé, ïî îïðåäåëåíèþ, ñîäåðæèò âñå áàçèñíûå ñèìâîëû: . ... 1 2 1 n e e e     (5.11)  àëãåáðå èäåé íóëåâîé ðàçìåðíîñòè 0 L åäèíè÷íàÿ èäåÿ íå ñóùå- ñòâóåò ââèäó îòñóòñòâèÿ â ìíîæåñòâå 0 S áàçèñíûõ èäåé. Äëÿ ëþáîãî n S x  ( n =1, 2, ....) âûïîëíÿåòñÿ ðàâåíñòâî , 1 1   x (5.12) íàçûâàåìîå çàêîíîì åäèíèöû. Äåéñòâèòåëüíî, åñëè x = 0, òî, ñîãëàñíî àêñèîìå íóëÿ, . 1 1 0   Åñëè æå x – íåíóëåâàÿ èäåÿ, òî îíà ìîæåò áûòü ïðåäñòàâëåíà â ôîðìå x = p i i i e e e    ... 2 1 , ãäå  p {1, 2,.., n }. Èñïîëüçóÿ àêñèîìû èäåìïîòåíòíîñòè, êîììóòàòèâíîñòè è àññîöèàòèâ- íîñòè, à òàêæå îïðåäåëåíèå åäèíè÷íîé èäåè (5.11), ïîëó÷àåì: 1  x = p i i i e e e    ... 2 1 n e e e     ... 2 1 = n e e e    ... 2 1 =1. Ðàâåíñòâî (5.12) îçíà÷àåò, ÷òî 1  x ïðè ëþáîì n S x  ( n =1, 2, ....). Òàêèì îáðàçîì, åäèíè÷íàÿ èäåÿ â ìíîæåñòâå n S – íàèáîëüøàÿ . Ïî- ñêîëüêó 0  1, òî 0  1. Çàìåòèì, ÷òî èç àêñèîì íóëÿ è êîììóòàòèâíîñòè âûòåêàåò åäèí- ñòâåííîñòü íóëåâîé èäåè. Äåéñòâèòåëüíî, ïðåäïîëîæèì, ÷òî ñóùåñòâó- þò èäåè 1 0 è 2 0 , óäîâëåòâîðÿþùèå àêñèîìå íóëÿ: х х   1 0 è у у   2 0 . 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CCvdЮx;!LSxξf.rwRdu& ?}ԛ<M:sjϯծRu8e_(SfmȜ˞ײG04z r\\0QS ˜yʜ'f592?{>i\S/o_ɷ@kvVa ˑQN diYKV(5τ&רr"=r͍r0HbL&" FE4^v嵪W_ytƨmd~a}^x,rqYY63ͿAn|221e iM=t7Sk0ݤqq2eK.yچk]P5ǀy*^`)]<df3yEɥWʦW( }I^V*nC ө +{wQА%n|s`Ce0HC;C2\0`S<°{V>-NOMƻÍ+d$WZsŹʹ1+a9p2pewez=_]sH~Ưݟ)h s}z#۶uFYsxi9= uݧΆ&\W Mkg31֌gO6J373\.;3 )Fe4ض z~zʶ\vr2߂pG2r"1ؾrymr{ٲr~}y5e2| cq9+@/0e=eBo_U7 w^:~r&oT^M`FHQ␣J/>>w3{ieY+,u/hVǸ1㷞0 '~@fH}^. V ˫/t|rmTchF}=Z uxLתdGj}uW,amRxn$i֓;Q3ⱋ* q[|v噶)<`Q>(`HKcLRM F|TjlUxZo1%Ux>z4F-]2~S_O|OH')Cd9rr'LmAm6h7 fn&/yHo< q<]yIzxe~ׅ2˧ ׉rE!{2z9/ى#EsqG<&ZtZedtw;>Q{%쁕ɣV5>Q#wي!yENi]͝ޞ{[y< uBjm,ǚ ~3׋=y'|/HwS},)24 .=NVr5zUp /犰>UA?q*,,F25 íèå y x z   êàêîé-íèáóäü èç èäåé n e e e ,..., , 2 1 . Îòñþäà âûòåêàåò, ÷òî 0  x è z x  . Ïîñëåäíåå æå íåâîçìîæíî. Âñå îñòàëüíûå èäåè ìíîæå- ñòâà z x  ðàçëîæèìû. Äåéñòâèòåëüíî, ëþáàÿ òàêàÿ èäåÿ ìîæåò áûòü ïðåäñòàâëåíà ñòàíäàðòíîé ôîðìîé p i i i e e e    ... 2 1 , â êîòîðîé èìååòñÿ, ïî êðàéíåé ìåðå, äâà ñëàãàåìûõ ( k 2 ). Ñîãëàñíî ïðèâåäåííîìó ðàíåå îïðåäåëåíèþ, áàçèñîì àëãåáðû èäåé n L ìîæåò ñëóæèòü ëþáîå ïîäìíîæåñòâî y ìíîæåñòâà n L , óäîâëåòâî- ðÿþùåå ñëåäóþùèì óñëîâèÿì: à) ìíîæåñòâî n B ñîñòîèò èç n èäåé; á) íóëåâàÿ èäåÿ íå ñîäåðæèòñÿ â ìíîæåñòâå n B ; â) èç íóëåâîé èäåè è èç èäåé ìíîæåñòâà . ) , ( 1 0 1 0 0 0 1 y x y x y x y x T    ìîæíî ñ ïîìîùüþ îïåðàöèè äèçúþíêöèè èäåé ïîëó÷èòü ëþáóþ èäåþ ìíîæåñòâà k . Ìíîæåñòâî { y x  } ÿâëÿåòñÿ áàçèñîì, ïîñêîëüêó îíî óäîâëåòâîðÿåò óñëîâèÿì à) - â). Äðóãèõ áàçèñîâ â àëãåáðå èäåé n L íå ñóùåñòâóåò. Äåéñòâèòåëü- íî, íè îäèí áàçèñ íå ìîæåò îáîéòèñü áåç âñåõ íàèìåíüøèõ íåíóëåâûõ èäåé ìíîæåñòâà n S , òàê êàê êàæäóþ èç ýòèõ èäåé íåâîçìîæíî ïðåäñòà- âèòü â âèäå ëîãè÷åñêîé ñóììû îòëè÷íûõ îò íåå èäåé, à ýòî âåäåò ê íåâûïîëíåíèþ óñëîâèÿ â). Äîáàâëåíèå êàêèõ-ëèáî èíûõ èäåé â ìíî- æåñòâî âñåõ íàèìåíüøèõ íåíóëåâûõ èäåé íåäîïóñòèìî, ïîñêîëüêó ÷èñëî èäåé â ìíîæåñòâå, ïîëó÷åííîì òàêèì ñïîñîáîì, ïðåâûñèò âåëè- ÷èíó n , à ýòî, â ñâîþ î÷åðåäü, ïðèâåäåò ê íåâûïîëíåíèþ óñëîâèÿ à). Èòàê, â àëãåáðå èäåé n L ñóùåñòâóåò åäèíñòâåííûé áàçèñ, è èì ÿâëÿåò- ñÿ ìíîæåñòâî n B ={ n e e e ,..., , 2 1 } âñåõ íàèìåíüøèõ íåíóëåâûõ èäåé n e e e ,..., , 2 1 ìíîæåñòâà n S . Îòñþäà íåïîñðåäñòâåííî ñëåäóåò, ÷òî â ìíîæåñòâå n S ñîäåðæèòñÿ âñåãî n íàèìåíüøèõ íåíóëåâûõ èäåé. Ðàññìîòðèì óñëîâèå: “ Äëÿ âñåõ n S y x  , èç c y x   ñëåäóåò c y x   “ (*). Óñëîâèþ (*) óäîâëåòâîðÿåò åäèíñòâåííûé ýëåìåíò ìíî- æåñòâà n S 0  с . Äåéñòâèòåëüíî, âåêòîð 0  с óñëîâèþ (*) óäîâëåòâî- ðÿåò, åñëè 0   y x , òî ñ íåîáõîäèìîñòüþ 0   y x , èíà÷å îêàçàëîñü áû, ÷òî 0  x èëè 0  y , ÷òî íåâîçìîæíî. Ïóñòü c – ëþáîé íåíóëåâîé ýëåìåíò ìíîæåñòâà n S . Ñîãëàñíî àêñèîìå íóëÿ, c c   0 . Òàêèì îáðà- çîì, èìååò ìåñòî ñëó÷àé, êîãäà c y x   , íî c x  , ÷òî ïðîòèâîðå÷èò óñëîâèþ (*). Èòàê, ìû äîêàçàëè, ÷òî âñå íåíóëåâûå âåêòîðû ìíîæåñòâà n S íå ïîä÷èíÿþòñÿ óñëîâèþ (*). 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Èññëåäîâàòåëü íå äîëæåí äîïóñêàòü, ÷òîáû èñïûòóåìûé âûíóæäåí áûë ãàäàòü, ÷òî æå èìåííî îçíà÷àåò ïðåäúÿâëåííûé åìó òåêñò. Îäíàêî òåêñòû, èìåþùèå íåñêîëüêî ðàçëè÷íûõ ñìûñëîâûõ çíà÷åíèé , äîïóñêàþòñÿ.  ýòîì ñëó÷àå ïîä ñìûñëîì òåêñòà ïîíèìàåòñÿ ñîâîêóïíîñòü âñåõ âîçìîæíûõ åãî ñìûñëîâûõ çíà÷åíèé. Ïðèìåðîì äâóñìûñëåííîãî òåêñòà ìîæåò ñëó- æèòü ôðàçà “ Äî÷ü áðàíèò ìàòü ” . Êàæäàÿ ìûñëü, âîçáóæäàåìàÿ èññëåäîâàòåëåì â óìå èñïûòóåìîãî, äîëæíà îäíîçíà÷íî îïðåäåëÿòüñÿ ïîðîæäàþùèì åå òåêñòîì. Ýòî òðåáî- âàíèå íàçîâåì óñëîâèåì ñìûñëîâîé îäíîçíà÷íîñòè òåêñòà . Îíî îçíà÷à- åò, ÷òî ïðè ïîâòîðíîì ïðåäúÿâëåíèè òåêñòà â óìå èñïûòóåìîãî äîëæíà âîçíèêíóòü òà æå ñàìàÿ ìûñëü. Ýòîãî ìîæíî äîñòè÷ü, åñëè êàæäûé òåêñò, ïðåäúÿâëåííûé èñïûòóåìîìó, áóäåò âîñïðèíèìàòüñÿ èì êàê èçîëèðîâàííûé . Òàêîé òåêñò íå äîëæåí ñâÿçûâàòüñÿ èñïûòóåìûì ñ êàêèì áû òî íè áûëî êîíòåêñòîì, âîîáùå – ñ êàêîé-ëèáî èíôîðìàöè- åé, êîòîðàÿ ìîãëà áû èçìåíèòü åãî ñìûñë. Íåâûïîëíåíèå óêàçàííûõ óñëîâèé ïðèâîäèò ê ïîòåðå èññëåäîâàòåëåì êîíòðîëÿ íàä ìûñëÿìè èñïûòóåìîãî.  ýòîì ñëó÷àå ýôôåêòèâíîå èçó÷åíèå ìåõàíèçìà ìûñëè- òåëüíîé äåÿòåëüíîñòè ÷åëîâåêà ñòàíîâèòñÿ íåâîçìîæíûì. Îòíîøåíèå ðàâåíñòâà, çàäàííîå íà ìíîæåñòâå n S , èíòåðïðåòèðóåì êàê ñïîñîáíîñòü èñïûòóåìîãî óñòàíàâëèâàòü ñîâïàäåíèå èëè ðàçëè÷èå ëþáûõ ìûñëåé, âîçíèêàþùèõ â åãî óìå. Ïîëüçóÿñü ýòîé ñïîñîáíîñòüþ èñïûòóåìîãî, èññëåäîâàòåëü âñåãäà ìîæåò ïðîâåðèòü âûïîëíåíèå óñëî- âèé ñìûñëîâîé îïðåäåëåííîñòè è îäíîçíà÷íîñòè òåêñòà. Ýòè óñëîâèÿ áóäóò âûïîëíÿòüñÿ, åñëè ëþáûå äâå ìûñëè, âîçáóæäàåìûå îäíèì è òåì æå òåêñòîì â óìå èñïûòóåìîãî, âñåãäà âîñïðèíèìàþòñÿ èì êàê èäåí- òè÷íûå. Ñóùåñòâóþò ðàçëè÷íûå òåêñòû, îáëàäàþùèå îäíèì è òåì æå ñìûñëîì. Òåêñòû, èìåþùèå îäèí è òîò æå ñìûñë, áóäåì íàçûâàòü òîæäåñòâåííûìè . Ïðèìåðîì òåêñòîâ ñ îäèíàêîâûì ñìûñëîì ìîãóò ñëóæèòü ïðåäëîæåíèÿ “ Èäåò äîæäü, èëè ñâåòèò ñîëíöå ” è “ Ñâåòèò ñîëíöå, èëè èäåò äîæäü ” . Âìåñòå ñ òåì, ñóùåñòâóþò òåêñòû, èìåþùèå ðàçíûå ñìûñëû. Íàïðèìåð, äëÿ ëþáîãî ÷åëîâåêà, âëàäåþùåãî ðóññêèì ÿçûêîì, ôðàçû “ Èäåò äîæäü ” è “ Ñâåòèò ñîëíöå ” èìåþò ðàçëè÷íûé ñìûñë. Âîçüìåì ïðåäëîæåíèå А “ Èäåò äîæäü ” è ïðåäëîæåíèå В “ Ñâåòèò ñîëíöå ” è îáðàçóåì èç íèõ ïðåäëîæåíèå С “ Èäåò äîæäü, èëè ñâåòèò ñîëíöå ” . Ñìûñë ïîñëåäíåãî ïðåäëîæåíèÿ ïðåäñòàâëÿåò ñîáîé ìíîæå- ñòâî òðåõ ñìûñëîâûõ çíà÷åíèé, âûðàæàåìûõ ôðàçàìè “ Èäåò äîæäü ” , “ Ñâåòèò ñîëíöå ” è “ Èäåò äîæäü, è ñâåòèò ñîëíöå ” . Ïðîäåìîíñòðèðî- âàííûé íà ýòîì ïðèìåðå ñïîñîá îáðàçîâàíèÿ ìûñëè с , çàäàííîé òåêñòîì С , èç ïðîèçâîëüíî âçÿòûõ ìûñëåé а è b , çàäàííûõ òåêñòà- ìè А è В , ðàññìàòðèâàåì êàê îïåðàöèþ äèçúþíêöèè b a c   àëãåáðû èäåé. Ñìûñë ïðåäëîæåíèÿ Ñ ðàññìàòðèâàåì êàê ëîãè÷åñêóþ ñóììó ñìûñëîâ ïðåäëîæåíèé А è В . 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C=l|lR6l"nCb 6i/< ޶4Rpހ⼛u7*&E{7-ڳn1NMqƅ=.O# |K^O[衻 ug:>k,|,duco-܃52oٹld@朅4{Ȳ1jYY rB̤~Bui;A6r]: #,kYXS+zrͮCV+odQw~b"ޝ |+| |-KB|1,>}N4wm]'je.JC[́s zM;7j&+όu4s-Z|box>) bgmmlFs6m`9gϜ n;A|>{(=3^c9cى9x:g 8Xρ(8O;.?R󡷊?֘GP·+7|vGt?joחF/_ݕO=AJ&~ǭμW|l>SXq M7㵏D9u|6E9D,ҿzDkԧ[] |T!rD7on|W~vUэѐ{,ZW+~zjOg2 柦dզ6eQȲ}[;FnOӧwKṽzOXk³矽߷i7ʍ{8:{=ſo^xFȽdi"c1:UgY+od:βV!|_VGP"q0>RBщK\.hu|3%e@,,28 çàäàííàÿ îïåðàöèÿ äèçúþíêöèè ìûñëåé ïîä÷èíÿåòñÿ àêñèîìàì èäåìïî- òåíòíîñòè, êîììóòàòèâíîñòè è àññîöèàòèâíîñòè. Ñîþç èëè ðàññìàòðèâà- åì êàê èìÿ îïåðàöèè äèçúþíêöèè ìûñëåé. Ñìûñë ëþáîãî ïðîòèâîðå- ÷èâîãî òåêñòà , íàïðèìåð, ôðàçû “ Èäåò äîæäü, è íå èäåò äîæäü ” , ðàññìàòðèâàåì êàê íóëåâóþ èäåþ. Òàêîé ñìûñë, êàê íåòðóäíî óáåäèòü- ñÿ, óäîâëåòâîðÿåò àêñèîìå íóëÿ. Ñìûñë ëþáîãî áåññîäåðæàòåëüíîãî òåêñòà, íàïðèìåð, ôðàçû “ Èäåò äîæäü, èëè íå èäåò äîæäü ” , ðàññìàòðè- âàåì êàê åäèíè÷íóþ èäåþ. Òàêîé ñìûñë ïîä÷èíÿåòñÿ çàêîíó åäèíèöû. Ïåðåõîäèì ê ðàññìîòðåíèþ âòîðîé ñîäåðæàòåëüíîé èíòåðïðåòàöèè àëãåáðû èäåé, íàçûâàåìîé íàìè ñèòóàöèîííî-ïðåäèêàòíîé. Áóäåì ôîð- ìàëüíî ïðåäñòàâëÿòü èñïûòóåìîãî â âèäå âïîëíå êîíå÷íîãî àâòîìàòà, çàäàâàåìîãî ôóíêöèåé ïåðåõîäîâ [5, c. 58] )) 1 ( ) 1 ( ( ) ( t- , V t- U G t U  (5.13) è ôóíêöèåé âûõîäîâ )) 1 ( ) 1 ( ( ) ( t- , V t- U H t V  . (5.14) Çäåñü t – òåêóùåå çíà÷åíèå äèñêðåòíîãî âðåìåíè , ò.å. òîò ìîìåíò, â êîòîðûé èññëåäîâàòåëü ïðîèçâîäèò î÷åðåäíîé îïûò íàä èñïûòóåìûì. Ìîìåíòû äèñêðåòíîãî âðåìåíè, ñëåäóþùèå íåïîñðåäñòâåííî äðóã çà äðóãîì, îáîçíà÷àåì ÷èñëàìè íàòóðàëüíîãî ðÿäà 0, 1, 2, .., m . Ìîìåíò 0 íàçûâàåì íà÷àëüíûì , ìîìåíò m – êîíå÷íûì .  ðîëè m ïðèíèìàåì äîñòàòî÷íî áîëüøîå íàòóðàëüíîå ÷èñëî. Ïåðåìåííàÿ t îïðåäåëåíà íà ìíîæåñòâå {0, 1, 2, …, m }. ×èñëî t -1 îáîçíà÷àåò ìîìåíò äèñêðåòíîãî âðåìåíè, íåïîñðåäñòâåííî ïðåäøåñòâîâàâøèé ìîìåíòó t .  ðîëè òàê- òà âðåìåíè, ò.å. èíòåðâàëà ôèçè÷åñêîãî âðåìåíè ìåæäó ñîñåäíèìè ìîìåíòàìè äèñêðåòíîãî âðåìåíè, ïðèíèìàåì äîñòàòî÷íî ìàëóþ âåëè- ÷èíó. Ñèìâîëîì ) (t U îáîçíà÷àåì ñîñòîÿíèå ïàìÿòè èñïûòóåìîãî â òåêó- ùèé ìîìåíò äèñêðåòíîãî âðåìåíè. Ñèìâîë ) (t V îáîçíà÷àåò ñîñòîÿíèå ôèçè÷åñêîãî ìèðà , îêðóæàþùåãî èñïûòóåìîãî, â òåêóùèé ìîìåíò. Âû- ðàæåíèÿ ) 1 (  t U è ) 1 (  t V îáîçíà÷àþò ñîñòîÿíèå ïàìÿòè èñïûòóåìîãî è ñîñòîÿíèå ôèçè÷åñêîãî ìèðà â ìîìåíò äèñêðåòíîãî âðåìåíè, íåïîñ- ðåäñòâåííî ïðåäøåñòâîâàâøèé òåêóùåìó ìîìåíòó. Ôóíêöèÿ ïåðåõîäîâ G îïèñûâàåò çàêîí, ïî êîòîðîìó ïàìÿòü èñïûòóåìîãî ïåðåõîäèò èç ñîñòîÿíèÿ ) 1 (  t U â ñîñòîÿíèå ) (t U â ðåçóëüòàòå äåéñòâèÿ íà èñïûòóå- ìîãî ôèçè÷åñêîãî ìèðà, íàõîäèâøåãîñÿ â ñîñòîÿíèè ) 1 (  t V . Ôóíêöèÿ âûõîäîâ H îïèñûâàåò çàêîí, ïî êîòîðîìó ôèçè÷åñêèé ìèð ïåðåõîäèò èç ñîñòîÿíèÿ ) 1 (  t V â ñîñòîÿíèå ) (t V â ðåçóëüòàòå äåéñòâèé èñïûòóå- ìîãî, îáóñëîâëåííûõ ñîñòîÿíèåì åãî ïàìÿòè ) 1 (  t U . s%xklUl[nmʣFQA&D " M$!L!M@ iJBQy,!b#E2^&=̝ X"3Yd \"3WdE!Z]bVo~$Lg fJu`KcPcI`Y9FkKo#Xl;h#aǃ:$pSIGJS݄KS##ۙB .lcô-`/d/e=D!9D{ľu9Q#`yLoGo=@Vw.ћlUXeEB.;3 Ȃ4)4=ͺSk>>'A!&呢`4߁tcO*g9 |9k梷G%}1@o^ҸM)WgIYu7c[(86Y$̳JϹN:8RɉK4Gp6g8J]x_&_._pi:1~mHGq܄nƕv2k!/]3{iۏً3}i H4&_K+GrRcA]Rצq~snCKyu_wYe Z'-o\=|>N%χ7l>c;]`#-eKυ7}ȕqןƲN:e`#+AT3oD+8+G6wm=>`~wٴ26 e9x)j `]SP؃F-㇥>Jmi28Xo;W ]&/)'[AFyYpc鏀Qce2lvBGΒ eCSV)^kuԭAo ^2٩2%*!'%rd,| ~csr^w#%-`.qpyhd7 *6gl ~1Ws>τc61ȓF8`eG1d;яALEė.f YZ3yxJ~rݍ9oe*\ oYFs}輋A%٭O3c=wxDZo[ԣmt;  k[WߋuǷv-8%Z໒jHrj 3ĩkӱ hzh/MDvuK{yUɻ|h}!+`ǧnk_kV}4Q#ZztpcOquրvԚݦmhcou\kDvv<K]7N瞛GkfhQӝQ~㽧wzWqwx16Ϙ;Ug6c8ork͵6w$Č6wwG6w/37;_jf_FOFm}3w59'Y\%YToHLyf (kF_~Tո ^^R5*# ."~";5( aRZbƞ>y/\З={$=U?ϪiȒTb\ r j/JǺRoUkEf_1dgw='_$'W}tjs6apHެX]>}ǁ=U+0֓"$Wt?CRHdž߲?_&\b@8T!ܩm6']_âqIUvޙ{Ӫmx3We?u\-8%mGo xHLԟ%hb(7LO=o.l737q!ow\xN&~g묩8 yayVys&B/t&mZN|7/|x\üI=u7)dg;y@$;d*C`uOoćU?S,?VmC\ҙǎG^&X,8P@'Q/x*6u(h_QS~tsHl瑢>4>2ʇUuTn]8uJrؼ,iFϞ=nIǥ~} m[㯨>cw٭S՞ߨ]r Saxz^&vx )exsZӒzzݚ˶[v+=$@7-TD ٭ל{ه_ZQ%rOgv~vKKkiļmem;@/#;+ضbcnW#{A1e +L& <_<YI6BْJJp2,i7,ŌOf<<.݂]3yT1Sx0)=QA&呧Z.~:m#؏=t _RCkWc_u[0#r3 EKze癚a~S/[oԐ޾YkW 4B.k[ٮ.F[35[G u"$$ka3x?4">Qtrߴukz_X|6m/ug:Ѿ:)nK]15/E>hKh_^by`S${!zuO^=}n^#.#7N>"{ӋDbMp^/brxJ1<"{%I?%<;e׳{M+tmf.͸q!yHx"k5kr*__::F/;OgGvo<;6[s+jf. !蕟5+|2vUf +Ы+3:S~Cw@>s"Y9zvƜk wvuwVv*fW[~<ݿϬ$X.bo>.zaOq&G@)*8 O4\F^\hZ;4*fa:k/*tAl-r]C>e ڗPZ;WsҾD臁E!{܏':yw q_]˥rM Jd1UE6zhZieL1WkN@6kZ2%4w73EWti#{4Fk4!'Z5ck.ێA ܪ1oInB/ )5u6lϭЫ[2Dkan?ј~9)v|Y  k|vA*n> ן ߬/<0nܧX3GR"ߦM٩װ,ҵHfZlc?cSs[Gk4y'v=ˁ> &-\O^>''j|ߧ| ?0'OY9sbl6*0O[[Go6=:i`"{A(?-wb|qզOe5KΔ_5ק*iP.iצgh#dӗH#~olzӮSr).}?{A@4t Ytɐ$6 p N#'rz|Ffs_g#i/\)8Rzj'n [K(ڹDi[ia:tz6>:Eu~[\Ƙ9x tMJ#")ZK e_n8n_nG)aƺY|tE lW7I#uCdo1˸3>OP>[\ʇhGU*2% vGenv7kVXEAd-]`O|z!@GF}Tm[ ,{o{=}${RGcvy/[۫'^5С]>P?NN[veo4b-{FP9Sr)vݴeO-k^% {, Kx[2,K^3ofV}@{@{hnG?vlNϊV˂T[#۽E[&|mqp'?kG86y(twM%veg;48RgxNU\+K[v\x!F5e':mݸN9ٚ&ܛiަu*`c\С/\ǁø@_8N exŸޏ3.u|ЋB݄CZS/Z2]6m*<1(V'W\u /F%JcpK"?^f= ߧ6Q}I.ys ~|3ɱ8 /,ZCj e1#_z/fua_oe|eQA1ܬ]R r47Ofكfoުf߹GM.'ܬ_:_:?!wܙ ::htMJU`9,~<s3Ÿo~3:~nށ-ϒX rt7|0f4ꖿ\ۮέg(s[9#,F\nz0Ud?Ke.t C'/P2.yK2WNTRN%9Rl>+{*|]5# u#2ךunw_Γ՞Kh{1݇Pu3XS}yDqK ru龟կ/bŚ;_aȑ=贫1_M#%%^=}]Wvu_4bއ&^R>lCgB'2f <Ïi_xl@>("(*.|M|(Y+Vj}'L;~*oRG.e8޲~>*- =_5^OH]/E~0~Ck뜢3WMI*;X4b-y~3ޡu|3 eR>iG~p)yeyYLXۣQY9EN6+gOzT2#h?iPVxolEܶ-䬢;~Q-{3r40ޖ rVp}&R즑طFҜI#rי/4FNʾ11]GLߘɇcz1Sy.PHy]HAxݳLN.ҿ =Џ/ ԫ A~w;ޥ!rO;޺u u(C;5+pNtH.;Y|¿PowC)aƺFNjܝ|tg~5`IHYR>lY dg(gJEmr?)^{P]8cYL9JJf<ƻ]Uݪ:|w«emH*mTౖ6֌'[O!=䔱밶el4bz}R>uL`U> ?KG[ƒO*Od,gDyK2}AXƮUdvo=*+ٛ}kU#;} {zا޻' ~"3 uG3E6;*^@=)dzLߤ4d:m =<f.Cd<%;!s,@EluU=ͫ}o3I#&~ٶlc[CFS749<_co7䜮O[r( {ykٍ|Ə\EV"Ƀ۪ ߢ~ѿ \pef'ʐekY,mU}e8qP_gl&/Fed-,ap2|)|yN2u("k|JeB lueT._;zGqS5>]|ɍW.>5z {"|~Aڏ~WM+}Wn ٗ,5^6G W*/ ]$O;$: [`txUBn3/FYx#;:3,,a Hgܠ7+yLyV_YauBՁDOXg煟8YLH#lYS3Rr\YQmRrb:e51/$[mDǹ ^ۺ߬Zl\-,rs>i{q\xH)z_sR*b=ty2pCk4#Śx 5ϨCy+S^_on^i o~=2oo5nX&oYh>Y/X 2;}S 1 Cd%un4! {}ڥN8›)`/~d5Wt=qrg K@.=ԭ[oP] YP.uiP EVrnUvqY^\8Еj̫5/>6Tm\HYq'7־*[y֨NIuVԿR&e1 οFv46ݯjWS 8}LmFoTI4_(mI:{F?< ~x x07=UpI#O::ԹK_tFnV>O*?4 k~ eN|7N>Sϴ\׏Gh/{=:K_ޞ+:Qm&lF*}Mכ$HL/x#R{:k_vQCz!l{Ȳm|9n_oF52kY~B @G|858g S1:(Ik>ᷦ6G2嗸DzXhڂuϿG{1cwcvErKoHjMj>A{a-iG# ?NL]ʅB'CzrEf߮Iwsоhcyh{-6c_YPӻ 4ad=#Ad<3.ig= [>>OM]8ű/Sm6f{2%@PAY=tچu\͢!^esh-(~RP*X2dː=$֝zz4b^otj1ޡ.p|R>iG#=Z2ìr40w|brKJcS+lY{X'-66.ytGؿv1ۤ6菤nB"Y7~,Miw:z^4M,];JRyKO=ӦAxR\8s';s +x5Gv~:Ѕ%x:xp7W|vcCP]wcxdM5G|AR~^W~)/~$_Uғx?OX&qGo|pc}?Bk 5 +ҳ*b__gZ_wĊ5=21~;jbHŚ@y<ҍwxb: ~ ~77(1g /l1Vcxayy /,"os[t"VA\2a!9gȞ9Mk4֡݋vsڥs"[~Lj|A9{*aOI1 /҅k`cشBf[^[~7N]CĻ7yf Bxחte픁+omPe2bxayPmX /O1? * l /wKMfCXxAyݻ}Ӣ^me5s/vI~7> evPѫGg{Ђ-ѱxYOsx:̋B-bxa/ 3"$ Jאݻg+4n?{{tkkl|}AнZ7!i;LA~]- z@ӦB+n@>dz\? xndgܜs{{] N{Pi:׫̵)c٠oj;6ح}1׸kxfL(66{\챱'#i?y_q% P%NsٔҷWaMJcۧqA OYd{oSŢZts[He~Ϲxcc.5_)7kOg뵻QPr^S&goL˥|z 7kkP葓#GAdZme@{pVF."{d-2YO:N_)4/Y/08X=6ym\;~u,Vwemb\|h/mc;ֶ/)"^n5gRl4<_RCd9Nx/eyiCPm<u7>.8Fh#yH^Ɵ8|G:m SYɇE>2vHҙ Ch:+TEݚr5N^c5Pvs}$6~frU\Udђ1c\+~ b\I' 1 \oM<PyzRB^]ܸ !3b64nS);u4 c mp<GE@<8YO{zwR{"\v3V7 N0N`o>QLQsbu#6Ҏ6`7@o/H?OX&3tO7֗[pjr{wNZ_2x{z|{݌}ūeInհo*F"D#8$#8Xg(Cg N;q^ҽ.v5osax b>&3o=_",8恷+1F[L۴,wtn賓[v=; he|³4U; ]qf7yf W֜EVcx)tllgbشBf"U7eF߰h[2yO_avlY C& W<^?ILv>kkvBYdw22[m`b'0-v8^9/'~ü/w y1&I/P᭨qG@q1Aiwi.N>xA'[5cM:ͿΔIG+:08v#k:iS予˗O=;?RZi}}ghɃrJoaUNpf+ov.ŗL/kiRyWVaA ^-rBkZiBã n!u$U[V^՘s,* /oEs=fhlB؆Azn*nb@V:{F|S@yV&+G0RDs|#֚9\5?Z|5 SLN *w 9@}`*9эW\Noa@/ыt_&q͆UT ؖnW^h* K!%X/i^GK(m5"d`H&R ?mUoIgD+녿*+,rﰢdN!_&_NeҺm''=Q˟-H>^3y D`]i,WpE+#2˽EYy]F:|ò6zzeQ%u$/﵊cJݙRۡP{ ߬:Bx= nayhҏ/j7宒Kd.]8lعJxN[3e]jzyQ=Һt~l7|DQ":%\'ZY'[~Bkkw$'xtv?xP4bf-y\_E-,9*Yr6e #&fb@fZv>J&wNA.#qCl?rVB^m[noR br|ޘDw/v"ߒߛa\݋ukrmi[nn鵯^0Gl+Ewhi#g݋FcfiLnč{&cyτDkpۺ ʸ{AEWm;VƧ6[w&<;}*ξk+ ]֓GUqshlLAlmی%a ־E锁W& [y@>מ=vwo_;uc/#lfiCl?w{9& ~_&`jr?.KqG%Ch*lY|'_>i/lT^Xܟ {HHc'0`64rÒ an3cVuN-}ckS0· Xk'-.cKah=O>\@R$we:4pM~”<ŧj<} p(tt9n WT21ZRT<g 4ܿHuAN\τ#!lLM!-*cX55[ 1Cqa+kSߧ mVXˤ7@ӮS6R>l lP!/K-YҐ37 KiVxߐ v٣'.lG”ie6O-u|( Q4| $A>*4M|AR=EI2cX/h) m)̱ w!8?}UW+4ꖿ\ٮgD1{F7aކ"λ*__Θ6O37k^X{{ǍvSqf+[o ڙҗ#2XKЗ@>֗7*n~{Dx9; -WGᖉho^rL譺gɏ~Cǂn<@C|5(<# <]v}n񤣫C;?qEt6k_j<BR] )ƾ~-'.)7BxݯXGW~#kV3޶u.8i|x93bʿrmw >˵ssJAN"> gw)O8$@^._= .`NwZC-{.xcbfNؠB e&xbzM\hWUfib6SGfʻY 4 1TDz@tHdέ[ΑV͜[nέ5Щ߄']v]e#*Z\ƪ={B<1=!bwk[he [3Q ߸b>?`NSbMΊ ᄚ GmZD-~G-RcxaW?bxa1hN6:njX]l/&ZV9^WI˱frݩ?x%PbЪ_ebB.sQWq2Q+V݉ܔdsE//;Lv;X*y]78KC?u,,529 Ñîñòîÿíèå ) (t U ïàìÿòè èñïûòóåìîãî â çàäàííûé ìîìåíò äèñêðåòíî- ãî âðåìåíè t áóäåì õàðàêòåðèçîâàòü ñ ïîìîùüþ íåêîòîðîãî ñëîâà [5, ñ. 75] r y y y T ... 2 1  , ïðåäñòàâëÿþùåãî ñîáîé ïîñëåäîâàòåëüíîñòü áóêâ r y y y ... 2 1 , âçÿòûõ èç äîñòàòî÷íî îáøèðíîãî àëôàâèòà R . Ïîëàãàåì, ÷òî äëèíà r ñëîâà T äîñòàòî÷íî âåëèêà è íå ìåíÿåòñÿ ñ òå÷åíèåì âðåìåíè. Êàæäîå ñëîâî áóäåì ôîðìàëüíî ïðåäñòàâëÿòü â âèäå áèíàðíîãî ïðåäè- êàòà ) , ( y x T , ãäå x – íîìåð [5, ñ. 115] áóêâû у â ñëîâå T (  х {1, 2, .., r }), у – áóêâà, ñòîÿùàÿ íà x -òîì ìåñòå â ñëîâå T ( R х  ). Ïîëàãàåì, ÷òî ïðåäèêàò T óäîâëåòâîðÿåò óñëîâèþ îïðåäåëåííîñòè 1 ) , (    y x T y x (5.15) è óñëîâèþ îäíîçíà÷íîñòè . 1 )) " ' ( ) " , ( ) ' , ( ( " '        y y y x T y x T y y x (5.16) Âñòðå÷àþùèéñÿ â âûðàæåíèè (5.16) ñèìâîë = îáîçíà÷àåò ïðåäèêàò ðàâåíñòâà áóêâ , çàäàííûé íà äåêàðòîâîì êâàäðàòå R R  . Ñîäåðæàòåëü- íî óñëîâèÿ (5.15) è (5.16) îçíà÷àþò, ÷òî íà êàæäîì ìåñòå â ñëîâå T ñòîèò îäíà-åäèíñòâåííàÿ áóêâà. Ïðåäèêàò T ìîæíî âûðàçèòü ñëåäóþùåé ôîðìóëîé àëãåáðû êîíå÷- íûõ ïðåäèêàòîâ [5, ñ. 113]: ). ( ... ) ( ) ( ) , ( 2 2 1 1 r r y y x y y x y y x y x T        (5.17) Áóäåì ñ÷èòàòü, ÷òî íà ÷àñòè ìåñò â ñëîâå T ñòîÿò íåçíà÷àùèå áóêâû [5, ñ. 118], êîòîðûå ñ òå÷åíèåì âðåìåíè ìîãóò çàìåùàòüñÿ çíà÷àùèìè áóêâàìè ïî ìåðå ïîñòóïëåíèÿ â ïàìÿòü èñïûòóåìîãî íîâîé èíôîðìà- öèè è çàïîìèíàíèÿ åå. Ïîëàãàåì, ÷òî, êðîìå çàïîìèíàíèÿ, âîçìîæåí è îáðàòíûé ïðîöåññ çàáûâàíèÿ ( óíè÷òîæåíèÿ [5, ñ. 110]) èíôîðìàöèè, êîãäà ïî ïðîøåñòâèè îïðåäåëåííîãî âðåìåíè íåêîòîðûå çíà÷àùèå áóêâû çàìåùàþòñÿ íåçíà÷àùèìè. Ìû ñ÷èòàåì òàêæå âîçìîæíîé çàìåíó âî âðåìåíè îäíèõ çíà÷àùèõ áóêâ äðóãèìè. Ïîñêîëüêó áóêâû r y y y ,..., , 2 1 ìîãóò ìåíÿòüñÿ âî âðåìåíè, áóäåì çàïèñûâàòü èõ, â ñëó÷àå íåîáõîäèìîñòè, â âèäå ) ( ),..., ( ), ( 2 1 t y t y t y r , ïîä÷åðêèâàÿ ýòèì òîò ôàêò, ÷òî îíè ÿâëÿþòñÿ ôóíêöèÿìè âðåìåíè. Òàê êàê ïðåäèêàò T çàâèñèò îò áóêâ r y y y ,..., , 2 1 , òî îí ìåíÿåòñÿ âî âðåìåíè. Æåëàÿ îòìåòèòü ýòî îáñòîÿòåëüñòâî, áóäåì çàïèñûâàòü ïðåäè- êàò T â âèäå t T . 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A)h}կ_a=mc ['>㦑N5p(mK"]½E=;+zkR5oj+To8+Bv[ y a\P:!nz uBAGPG{#J%ރXG\zv庫m?KٰuxeguqŊC?l9=nH$]--|fvd,r{W[OZ2&h4[-:}+X#p;yp~hÚ6hkǠ ߈k f}"z…{W enq":giN@<)ԃ[ն Վ#ErɃ4zxN(I/'yh?<"0_fI:?A-+$%~5+SϥO!> ˄'NKJ)MѽJ ,Cy@c=Z|`D{SnO] ju X>.閄|_g-,aA'K e waȂAxXHzI nO z  R,~Nm]5#CYlewIGG"K,nnMү/}+ 69˥lزblb@5chmߊSةEֲ6e=EpGUMg\qgR$쬴~KMu4μ5Jݡ: [7qWڏjM',!Շ`04" aBR|m7%6O'w@I^+<"6!~V@ l2VRSi@tR6l$:~ d2BYL\3)Q'3K,{ #/bk,RZ|E.c;Cs(c@>^(=-3s=C+mq/J#L{ow@u6/}Bű;Gá]@y_?_\,,30 ×åëîâåê íå ìîæåò îäíîâðåìåííî îñîçíàâàòü ñðàçó âñþ èíôîðìàöèþ, õðàíÿùóþñÿ â åãî ïàìÿòè.  êàæäûé ìîìåíò âðåìåíè åìó äîñòóïíà ëèøü íåêîòîðàÿ ÷àñòü ñîäåðæèìîãî ïàìÿòè.  ñîîòâåòñòâèè ñ ýòèì ââåäåì ïðåäèêàò ) (t Q t , êîòîðûé âûäåëÿåò [5, ñ. 107] â ñëîâå ) , ( y x T t ÷àñòü ìåñò , îñîçíàâàåìûõ èñïûòóåìûì â ìîìåíò âðåìåíè t . Âîñïðè- íèìàåìàÿ ñîçíàíèåì èñïûòóåìîãî ÷àñòü [5, ñ. 121] ) , ( y x P t ñëîâà ) , ( y x T t , ñòîÿùàÿ íà ýòèõ ìåñòàõ, îïðåäåëÿåòñÿ ôîðìóëîé [5, ñ. 123]: ). , ( ) ( ) , ( y x T x Q y x P t t t   (5.19) Âûäåëåíèå ÷àñòè ñëîâà ìîæíî ïðåäñòàâèòü â âèäå ïðîöåäóðû, âû- ïîëíÿåìîé ñ ïîìîùüþ ðåãóëèðóåìîãî ñåëåêòîðà [5, ñ. 105]. Âîñïðèíèìà- åìóþ ñîçíàíèåì èñïûòóåìîãî ÷àñòü ) , ( y x P t ñîäåðæèìîãî åãî ïàìÿòè áóäåì íàçûâàòü ñèòóàöèåé . Çàäàíèå èñïûòóåìîìó íà âîñïðèÿòèå èì òîé èëè èíîé ñèòóàöèè äàåò èññëåäîâàòåëü. Íàïðèìåð, èññëåäîâàòåëü ìîæåò ïðåäëîæèòü èñïûòóåìîìó ïîñìîòðåòü â îêíî íà îòêðûâàþùèéñÿ âèä íà óëèöó, âñïîìíèòü îäíî èç â÷åðàøíèõ ñîáûòèé èëè ìîòèâ êàêîé- íèáóäü ïåñíè, îáðàòèòü âíèìàíèå íà ñâîå ñàìî÷óâñòâèå èëè íàñòðîå- íèå. Ìû ïîëàãàåì, ÷òî îáðàçû ïðåäìåòîâ âíåøíåãî ìèðà, ôîðìèðóåìûå îðãàíàìè ÷óâñòâ, íåïîñðåäñòâåííî íàøèì ñîçíàíèåì íå âîñïðèíèìàþò- ñÿ. Îíè ñíà÷àëà çàïîìèíàþòñÿ è ëèøü ïîñëå ýòîãî ìîãóò îñîçíàâàòüñÿ. Îáðàçóåì ìíîæåñòâî âñåâîçìîæíûõ ñèòóàöèé N è ââåäåì ïåðåìåí- íóþ Х íà ýòîì ìíîæåñòâå. Áóêâîé Y áóäåì îáîçíà÷àòü èäåè èç ìíîæå- ñòâà n S . Ïðåäïîëîæèì, ÷òî èññëåäîâàòåëü ïðåäúÿâëÿåò èñïûòóåìîìó ñèòóàöèþ Х è èäåþ Y è ïðåäëàãàåò åìó îïðåäåëèòü, ðåàëèçóåòñÿ ëè â ñèòóàöèè Х èäåÿ Y . Íàïðèìåð, èññëåäîâàòåëü ïðîñèò èñïûòóåìîãî âçãëÿíóòü â îêíî íà óëèöó è îòâåòèòü íà âîïðîñ, èäåò ëè òàì äîæäü. Åñëè äîæäü äåéñòâèòåëüíî èäåò, òî èñïûòóåìûé äîëæåí îòðåàãèðîâàòü îòâåòîì “ äà ” , â ïðîòèâíîì ñëó÷àå – îòâåòîì “ íåò ” . Ñâîèì ïîâåäåíèåì èñïûòóåìûé ðåàëèçóåò íåêîòîðûé ïðåäèêàò ) , ( Y X L Z  , çàäàííûé íà äåêàðòîâîì ïðîèçâåäåíèè n S N  .  íàøåì ïðèìåðå â ðîëè ñèòóàöèè Х âûñòóïàåò âîñïðèÿòèå èñïûòóåìûì óëèöû, ðîëü èäåè Y èãðàåò ñìûñë ôðàçû “ Èäåò äîæäü ” .  ðîëè íóëåâîãî çíà÷åíèÿ Z =0 ïðåäèêàòà L âûñòóïàåò îòâåò èñïûòóåìîãî “ íåò ” , â ðîëè åäèíè÷íîãî çíà÷åíèÿ Z =1 – îòâåò “ äà ” . Çíà÷åíèå Z ïðåäèêàòà L ïðèìåì çà èñòèííîñòíîå çíà÷åíèå âûñêàçûâàíèÿ, çàäàþùåãî èäåþ Y .  íàøåì ïðèìåðå â ðîëè òàêîãî âûñêàçûâàíèÿ âûñòóïàåò ïðåäëîæåíèå “ Èäåò äîæäü ” . Åñëè Z =1, òî âûñêàçûâàíèå, çàäàþùåå èäåþ Y , ñ÷èòàåì èñòèííûì äëÿ ñèòóàöèè х , åñëè æå Z =0, òî – ëîæíûì . Ïðåäèêàò L íàçûâàåì ñèòóàöèîííî-ñìûñëîâûì . 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Îáîçíà÷èì ýòîò ïðåäèêàò ñèìâîëîì ), , ( ) ( A X L X L A  (5.20) íàçûâàÿ åãî ñèòóàöèîííûì ïðåäèêàòîì , ñîîòâåòñòâóþùèì èäåå А . Î÷åâèäíî, ÷òî ðàçíûì èäåÿì B A  ñîîòâåòñòâóþò ðàçëè÷íûå ïðåäèêà- òû A L è B L , ) ( X L A ) ( X L В . Äåéñòâèòåëüíî, âñåãäà ìîæíî ïîäîáðàòü òàêóþ ñèòóàöèþ C X  , â êîòîðîé èäåÿ А ðåàëèçóåòñÿ, à èäåÿ B – íåò, ò.å. ) ( ) ( C L C L B A  . Âìåñòå ñ òåì, ðåàêöèè èñïûòóåìîãî íà ëþáóþ ñèòóàöèþ Х , ñîîòâåòñòâóþùèå òîæäåñòâåííûì òåêñòàì, èìåþùèì îäèí è òîò æå ñìûñë А , î÷åâèäíî, âñåãäà áóäóò îäèíàêîâûìè. Ýòî îçíà÷àåò, ÷òî ìåæäó ëþáîé èäååé n S A  è ñîîòâåòñòâóþùèì ýòîé èäåå ñèòóàöèîííûì ïðåäèêàòîì ) ( X L A ñóùåñòâóåò âçàèìíî-îäíîçíà÷íîå ñîîòâåòñòâèå. Òàêèì îáðàçîì, ïðåäèêàò ) ( X L A ìîæåò âûñòóïàòü â ðîëè ïîëíîé õàðàêòåðèñòèêè èäåè А . Îïèñàííóþ èíòåðïðåòàöèþ àëãåáðû èäåé íàçîâåì ñèòóàöèîííî-ïðåäèêàòíîé . Ìû ïîëó÷èëè âòîðóþ èíòåðïðåòàöèþ àëãåáðû èäåé, òåñíî ñâÿçàí- íóþ ñ ðàíåå ðàññìîòðåííîé ñìûñëîâîé èíòåðïðåòàöèåé. Òåïåðü â ðîëè ìíîæåñòâà n S âûñòóïàåò ìíîæåñòâî âñåâîçìîæíûõ ïðåäèêàòîâ ) ( X L A , ïðè÷åì êàæäîé èäåå А âçàèìíî-îäíîçíà÷íî ñîîòâåòñòâóåò ñèòóàöèîí- íûé ïðåäèêàò ) ( X L A . Òàê êàê ìíîæåñòâî âñåõ ñèòóàöèé êîíå÷íî, òî ìíîæåñòâî n S âñåõ ñèòóàöèîííûõ ïðåäèêàòîâ ) ( X L A êîíå÷íî. Ýòî îçíà÷àåò, ÷òî ÷èñëî âñåõ èäåé, êîòîðûìè ìîæåò îïåðèðîâàòü èñïûòóå- ìûé, êîíå÷íî. Îïåðàöèè äèçúþíêöèè B A  ñîîòâåòñòâóåò äèçúþíê- öèÿ ) ( ) ( X L X L B A  ñèòóàöèîííûõ ïðåäèêàòîâ A L è B L . Î÷åâèäíî, ÷òî îïåðàöèÿ äèçúþíêöèè ñèòóàöèîííûõ ïðåäèêàòîâ èäåìïîòåíòíà, êîììóòàòèâíà è àññîöèàòèâíà, â ñèòóàöèîííî-ïðåäèêàòíîé èíòåðïðåòà- öèè àêñèîìû èäåìïîòåíòíîñòè, êîììóòàòèâíîñòè è àññîöèàòèâíîñòè àëãåáðû èäåé âûïîëíÿþòñÿ. Íóëåâîé èäåå 0 ñîîòâåòñòâóåò òîæäåñòâåí- íî-ëîæíûé ñèòóàöèîííûé ïðåäèêàò 0 ) ( 0  X L , åäèíè÷íîé èäåå 1 ñîîò- âåòñòâóåò òîæäåñòâåííî-èñòèííûé ñèòóàöèîííûé ïðåäèêàò 1 ) ( 1  X L . ßñíî, ÷òî àêñèîìà íóëÿ è çàêîí åäèíèöû â ñèòóàöèîííî-ïðåäèêàòíîé èíòåðïðåòàöèè àëãåáðû èäåé âûïîëíÿþòñÿ. 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۰׺.p9/T_~X@SїZڿBi@kW{֬ϰW-*;8çjFq{wQ/s>A<ƙ^ ׯ۠*L>e['y`./a'7_4['KIJ(['i\/8bi(tԤf^{/7|ۧ)e|\׮mJĴ|)E2nRPLҐȤ<'oKme#b||WfID ˆ#U yBYB yF䐉7(!~U0u;Kfc6+_S-enr`k^ ZT|)lxHk^K&ͭf[& /s6mP 4Ykf׼E}8o]:svkݿTzMfߖ >`ya9ٴ쬽5pQ>!GrvKAz@xkķ趆gGpZVZ#U6ېwC$߫@#{Y@ٌ`xPt V>eYc# S:(m ϸ lX70\es|S_* _ 6[<:()u7Ci}40=6n;v~N,,32 . 1 )) ( ) ( (    X L X L X B A (5.22) Îáðàòíî, åñëè âûïîëíåíî óñëîâèå (5.22), òî áóäåò òàêæå âûïîëíÿòü- ñÿ óñëîâèå (5.21). Òàêèì îáðàçîì, îòíîøåíèå ÷àñòè÷íîãî ïîðÿäêà B A  èäåé A è B èíòåðïðåòèðóåòñÿ êàê îòíîøåíèå âêëþ÷åíèÿ ) ( ) ( X L X L B A  ñîîòâåòñòâóþùèõ èì ñèòóàöèîííûõ ïðåäèêàòîâ. Êàæ- äîé íåíóëåâîé ìèíèìàëüíîé èäåè ñîîòâåòñòâóåò ñèòóàöèîííûé ïðåäè- êàò, îáðàùàþùèéñÿ â åäèíèöó òîëüêî íà îäíîé åäèíñòâåííîé ñèòóà- öèè. Òàêèì îáðàçîì, êàæäîé áàçèñíîé èäåå A ñîîòâåòñòâóåò ñèòóàöèîí- íûé ïðåäèêàò ) ( X L A , óäîâëåòâîðÿþùèé óñëîâèþ . 1 ) ( !   X L Х A (5.23) Ñèòóàöèîííûé ïðåäèêàò n B , óäîâëåòâîðÿþùèé óñëîâèþ (5.23), áóäåì íàçûâàòü áàçèñíûì . Î÷åâèäíî, ÷òî äèçúþíêöèÿ âñåõ áàçèñíûõ ñèòóàöèîííûõ ïðåäèêàòîâ ðàâíà òîæäåñòâåííî-èñòèííîìó ñèòóàöèîí- íîìó ïðåäèêàòó, òàê ÷òî çàêîí èñòèííîñòè ñèòóàöèîííî-ïðåäèêàòíîé èíòåðïðåòàöèè âûïîëíÿåòñÿ. ×èñëî c c   0 èíòåðïðåòèðóåì êàê ÷èñëî âñåõ ñèòóàöèé, ñîäåðæàùèõñÿ â ìíîæåñòâå N . ×èñëî âñåõ ñèòóàöèîí- íûõ ïðåäèêàòîâ, çàäàííûõ íà ìíîæåñòâå n S , ðàâíî n 2 , ÷òî ñîãëàñóåòñÿ ñ ñîîòâåòñòâóþùèì òðåáîâàíèåì â îïðåäåëåíèè àëãåáðû èäåé. Î÷åâèä- íî, ÷òî ëþáîé ïðåäèêàò ) ( X L A ìîæíî ïðåäñòàâèòü â âèäå äèçúþíêöèè íåêîòîðûõ áàçèñíûõ ïðåäèêàòîâ, òàê ÷òî àêñèîìà n -ìåðíîñòè âûïîë- íÿåòñÿ. Ïåðåéäåì òåïåðü ê ðàññìîòðåíèþ òðåòüåé ñîäåðæàòåëüíîé èíòåðïðå- òàöèè, êîòîðóþ íàçîâåì ñèòóàöèîííî-ìíîæåñòâåííîé .  ýòîé èíòåð- ïðåòàöèè â ðîëè ýëåìåíòà ìíîæåñòâà n S , ñîîòâåòñòâóþùåãî èäåå А , ïðèíèìàåì ìíîæåñòâî A M âñåõ ñèòóàöèé, óäîâëåòâîðÿþùèõ óñëîâèþ . 1 ) (  X L A (5.24) Äèçúþíêöèè В А  èäåé А è В â äàííîé èíòåðïðåòàöèè ñîîòâåò- ñòâóåò îáúåäèíåíèå A A M M  ìíîæåñòâ A M è В M . Íóëåâîé èäåå ñîîòâåòñòâóåò ïóñòîå ìíîæåñòâî ñèòóàöèé, åäèíè÷íîé èäåå – ìíîæå- ñòâî N âñåâîçìîæíûõ ñèòóàöèé. Îòíîøåíèþ ÷àñòè÷íîãî ïîðÿäêà В А  èäåé А è В ñîîòâåòñòâóåò îòíîøåíèå âêëþ÷åíèÿ A A M M  ìíîæåñòâ A M è В M . Ìíîæåñòâî âñåõ èäåé n S èíòåðïðåòèðóåì êàê ñèñòåìó âñåõ ïîäìíîæåñòâ ìíîæåñòâà N . 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Äåëî â òîì, ÷òî áàçèñ àëãåáðû èäåé, ñîñòîÿùèé èç áàçèñíûõ ýëåìåíòîâ n e e e ,..., , 2 1 è áàçèñíîé îïåðàöèè  äèçúþíêöèè èäåé, áûë íàìè âûáðàí ïî ñóùåñòâó ñëó÷àé- íî è áåç ó÷åòà îñîáåííîñòåé ñòðóêòóðû òåêñòîâ åñòåñòâåííîãî ÿçûêà. Î÷åâèäíî, ÷òî âîçìîæíû ìíîãèå ðàçëè÷íûå âàðèàíòû îïðåäåëåíèé, çàäàþùèõ ðàâíîñèëüíûå äðóã äðóãó àëãåáðû èäåé, îñíîâàííûõ íà èíûõ áàçèñíûõ ýëåìåíòàõ è áàçèñíûõ îïåðàöèÿõ. Âåðîÿòíîñòü òîãî, ÷òî â òåêñòàõ åñòåñòâåííîãî ÿçûêà ôàêòè÷åñêè ðåàëèçîâàíî èìåííî òî îïðå- äåëåíèå àëãåáðû èäåé, êîòîðîå áûëî âûáðàíî íàìè, âåñüìà íåâåëèêà.  ñâåòå ñêàçàííîãî ïðåäñòàâëÿåòñÿ öåëåñîîáðàçíûì ïðîàíàëèçèðîâàòü ñòðóê- òóðó òåêñòîâ åñòåñòâåííîãî ÿçûêà íà ïðåäìåò âûÿñíåíèÿ òîãî, êàêîé êîíêðåòíî íàáîð áàçèñíûõ ýëåìåíòîâ è îïåðàöèé ôàêòè÷åñêè â íèõ èñïîëüçóåòñÿ. Åñëè ýòî óäàñòñÿ ñäåëàòü, òî ìîæíî áóäåò â ñîîòâåòñòâèè ñ ïîëó÷åííûìè ðåçóëüòàòàìè ðàçðàáîòàòü äðóãîé, ðàâíîñèëüíûé èñõîä- íîìó, âàðèàíò îïðåäåëåíèÿ àëãåáðû èäåé, äîïóñêàþùèé áîëåå ãëóáî- êóþ åå ñîäåðæàòåëüíóþ èíòåðïðåòàöèþ. Ñïèñîê ëèòåðàòóðû: 1. Äóäàðü Ç.Â., Êàëèíè÷åíêî Î.Â., Øàáàíîâ-Êóøíàðåíêî Ñ.Þ. O ìåòîäå è çàäà÷àõ òåîðèè èíòåëëåêòà. IV. ÀÑÓ è ïðèáîðû àâòîìàòèêè. 2000. Âûï. 111. Ñ. 130-155. 2. ßáëîíñêèé Ñ.Â. Ââåäåíèå â äèñêðåòíóþ ìàòåìàòè- êó. Ì.: Íàóêà. 1979. 395 ñ. 3. Øàáàíîâ-Êóøíàðåíêî Þ.Ï. Òåîðèÿ èíòåëëåêòà. Ìàòåìàòè÷åñêèå ñðåäñòâà. Õ.: Âèùà øê. Èçä-âî ïðè Õàðüê. óí-òå, 1984. 144 ñ. 4. Ìàëüöåâ À.È. Àëãåáðàè÷åñêèå ñèñòåìû. Ì.: Íàóêà, 1970. 476 ñ. 5. Øàáàíîâ- Êóøíàðåíêî Þ.Ï. Òåîðèÿ èíòåëëåêòà. Òåõíè÷åñêèå ñðåäñòâà. Õ.: Âèùà øê. Èçä-âî ïðè Õàðüê. óí-òå, 1986. 136 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 20.04.2000 Äóäàðü Çîÿ Âëàäèìèðîâíà, êàíä. òåõí. íàóê, ïðîôåññîð, è.î. çàâ. êàô. ÏÎ ÝÂÌ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäå- ëèðîâàíèå ÿçûêîâûõ ìåõàíèçìîâ ÷åëîâåêà. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-94-46. Êàëèíè÷åíêî Îëüãà Âëàäèìèðîâíà, àñïèðàíòêà êàô. ÏÎ ÝÂÌ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòèêà, ïðîãðàììèðîâàíèå. Àä- ðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-94-46. 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M&/Ԯf5HO/VzNڗdi~Cr?sHf紏fd[u(gM8˯qtLɹ򷌞d>7Y9==vtn@p̞=2B/VF=7?xiDwOsz}OE)y*y"9fd%94\[ [IڶSm?4g7^k.;+BoֳOgo"Kɽw%Jj!xm)eQ}ש݅5×r.Rs>^Go(X9Wm}–-j|>ɟEg 5٤y4"z>BZL}I[ ,z%rEƖ2Rv8/5sk'q}3k}I>1jЭׄoKvG#2iD'扯םXj[wM#rf´\vHIO$J;+w GiOE?8ϋϪF>Gy)>A||p%t%o~?7_q6Dz3PU=  Է;CT6(mQ~~Ϙo߳9~pcϊ73dgP;:$JDO# qBW=QFʓvyng)ó].~nƩ RHd!*rd-u\UN^wXWqXK5_ÿÇ;Jt}>B %`[ e,yvQ%H?DH1S^l ] +佬|'C;xɳSw'<ϗ'RJ7g5.ƙM\||dbd>Ao!?]-WC}2A4S/{y6wyF/t1_7iPJ?UA 3i-oPW}^1Ww=*ւg_}.9K:eGΘ _v*~R|=a>E_6c;C(m St"Sj_Sli=t!L>uN§wwW/؈Jd-?1v wPYzW|ӚStˢnOI5>WFcnD^ܗG}jcl_D/]| ^+ӱ N1R0K\]?ynp}O$|zSS0D}ߓE3&%9}|P12]C>*d3K>H66RF_0VrSˀqoWC&iI򆞺AK|$NDe}L5ՍxNW`<%mrr^,, 35 ÓÄÊ 519.237.8 Â.Ì ÁÅÇÐÓÊ, Þ.Í ÃÎËÎÁÎÐÎÄÜÊÎ ÂÅÊÒÎÐÍÀß ÎÏÒÈÌÈÇÀÖÈß ÓÑÒÐÎÉÑÒ ÐÀÑÏÎÇÍÀÂÀÍÈß ÑËÓ×ÀÉÍÛÕ ÑÈÃÍÀËΠÏÐÈ ÍÀËÈ×ÈÈ ÊËÀÑÑÀ ÍÅÈÇÂÅÑÒÍÛÕ ÑÈÃÍÀËΠÐàññìàòðèâàåòñÿ çàäà÷à ðàñïîçíàâàíèÿ çàäàííûõ ñèãíàëîâ ïðè íàëè÷èè êëàññà íåèçâåñòíûõ ñèãíàëîâ, êîòîðàÿ ÿâëÿåòñÿ ÷àñòíûì ñëó÷àåì çàäà÷è ìíîãîàëüòåðíàòèâíîãî îáíàðóæåíèÿ ñèã- íàëîâ â óñëîâèÿõ ïîâûøåííîé àïðèîðíîé íåîïðåäåëåííîñòè.  òðàäèöèîííûõ çàäà÷àõ ðàñïîçíàâàíèÿ îáû÷íî ïîëàãàåòñÿ, ÷òî ÷èñëî ïðîâåðÿåìûõ ãèïîòåç ñîâïàäàåò ñ ÷èñëîì ðàñïîçíàâàåìûõ ñèãíà- ëîâ [1,2]. Îäíàêî íà ïðàêòèêå ÷àñòî êðîìå çàäàííûõ â ñòàòèñòè÷åñêîì ñìûñëå ñèãíàëîâ íà ðàñïîçíàâàíèå ïðåäúÿâëÿþòñÿ íåèçâåñòíûå ñèãíà- ëû [3,4]. Êðîìå òîãî, òðåáîâàíèÿ ïðàêòè÷åñêîé ðåàëèçóåìîñòè îïðåäå- ëÿþò íåîáõîäèìîñòü îïòèìèçèðîâàòü ðåøåíèå çàäà÷è ïî ñîâîêóïíîñòè ïîêàçàòåëåé êà÷åñòâà ðàñïîçíàâàíèÿ è çàòðàò íà ðåàëèçàöèþ. Ðàññìîò- ðèì ïðèìåð îïòèìèçàöèè äàííîé çàäà÷è ðàñïîçíàâàíèÿ ïî âåêòîðíîìó êðèòåðèþ, âêëþ÷àþùåìó ñîâîêóïíîñòü ïîêàçàòåëåé êà÷åñòâà ðàñïîçíà- âàíèÿ ñèãíàëîâ, à òàêæå çàòðàò íà ïðîåêòèðîâàíèå è ðåàëèçàöèþ óñòðîéñòâ ðàñïîçíàâàíèÿ. 1. Ïîñòàíîâêà çàäà÷è Ïóñòü ðàñïîçíàâàíèþ ïîäëåæàò M ãàóññîâñêèõ ñëó÷àéíûõ ñèãíà- ëîâ, ïðåäñòàâëåííûõ êîíå÷íîìåðíûìè âåêòîðàìè M i X i , 1 ,   . Ââåäåì 1  M -íó ãèïîòåçû: M i H i , 1 ,  – î äåéñòâèè çàäàííûõ â ñòàòèñòè÷åñ- êîì ñìûñëå ñèãíàëîâ; 1  M H – î äåéñòâèè 1  M -ão êëàññà íåèçâåñò- íûõ ñèãíàëîâ. Çàäàäèì àïðèîðíûå âåðîÿòíîñòè ãèïîòåç i i P H P  ) ( , ïðè÷åì     1 1 1 M i i P . Ïëîòíîñòè âåðîÿòíîñòè ñèãíàëîâ   M i H X N i i , 1 , , /     èçâåñòíû íå- ïîëíîñòüþ ñ òî÷íîñòüþ äî âåêòîðíîãî ïàðàìåòðà 1   , îäíàêî ìîãóò áûòü ïîëó÷åíû îáó÷àþùèå âûáîðêè ýòèõ ñèãíàëîâ . , 1 , , 1 , M i n r X i i r    1  M -é êëàññ ïðåäñòàâëÿåò ñìåñü íåèçâåñòíûõ ñèãíàëîâ, î êîòîðûõ íåò àïðèîðíûõ äàííûõ, çà èñêëþ÷åíèåì óòâåðæäåíèÿ î ðàçëè÷èè ñòàòèñòè- ÷åñêèõ õàðàêòåðèñòèê çàäàííûõ è íåèçâåñòíûõ ñèãíàëîâ. xklTU.[RJ, W+@E ) $&Ђ ZkeEm%jX A BbAp;M-h̙98sn5QDҽ"="'Ai8~ì0DV-ﮞexWc~[Wh29Yrh`]lɓq{!X7~+Wl,) ,1oZS۫M,X%.5H/s\VUdfCC/́T9ҤF$g v [Nl NSOzPz"e h͒T9{'_U(~FRO YƾjAOiMݠL$P./kV }^Os5c.?mJP`]H~{(1g38>7Y5;35b-CF`kIqzm}2ʑ"U+QRFԝỊ|ڜ-&r卛y%2vI-åMEɓ.zG{<{W*Ws6N,XQd?A+Omkd{ƎuOʖvzu|kDC}փSe'r$[S5`l%Ø^-KM@i}̙goPt h-ޏ|Լ0ؒ9gb;uunݟ;hSO֩YhTVC&ӭ>+yZg3R)=l㼏?y G߄WN`(Ӱcog[Lު[)9dK%f7 'ZB.o\Ad}9F}#~bsxksAW, %BA eqװ7Ld,f"H7k|[ k\: d:yǾ`9 rT7uR_IP3"o1+Qr_~v`Z?CS3L/6{Gh< {5<|}vuWL\6>wRBtzzGenZs3/LML"1RMBxl3: 4ydI:#G#a˫<󨳃ժ~ S,z&q$s&sG<7rG8Q#y[C<# qWGBΤ=R̍F q_^sp ~#; cy }ې&d%!HV<L0=p#4q~59\]Kk9N=/]c$h>nl>7"jtӹ^q:[s=ӷsF7Ӭ54Noy.ꬩug8ߑƦcMguNiMnsO];.t͑#ٍ kME#P1n`!`.eb+6 )pbI[ ;`b;w1H HˆC{oz~s$+t_>{mKFc$ɽ _<(I=D5$&I*| IڒWI.w* p+C_tR[Gg7MM&&$K$O/ 5-Im5o~2+RWc=mUyzUZ[w+9FUT/Tj.=e389N^~ EhK!ezI!{usٻwoҕof"KZvFk@_⺒\xmRQݏ+ Q̵gKNdFp{߱YL{`(̕)*OVi >2Ykg+S}j[5͊Z↡o^ޗii۹1hgܶK.x/u*{+99u;wt%c{V&ݗ7d1}oW]ʣ۴/L>tκ G>wx|O::*/x0+ReKSLKX2ԣ?9 ʇ=GR=ko(ojE oϛjbD)bEțs絵 Ibxuh&$_K^V [S ]~rFvJ?lST:PQe7rUg`N-uymx±S 35dGY򐱱TjVOiN.3=>13b+ B3]SgB-Lc{Zc8鏔WO?6)im쫥}wp\+㟺U+5OY$9 Ƞ[WBkCNS22B) MG?JԮ'sMV?dS+iN~' }!fzk^ԩE/oԛ:6Lg7sH/Gl>m>̚)G%?FL^] {֢vGT'Ѹ]ML`ZdlJlsr~ܽzzʞ-5RKr>L%J :c͘s#ZS'㺻C856vU;ӋU\_*kMygn_y'^ 쟕booe? _!hkʜ`n-dhһS-guf[Y56A x!1xqqJ8#%uV׺G/3j9U}3bE:_%iMpnpB ,x dUE+4Tob_D>Ƿ†􃣵23:Kچ.sӢtqO׆G~]4Fh-&kCgõF[w'wg/J`uR@/T-ZMJ6?T]c9BԳdK6ٻ'cQ"<&Qmk(_WIf.X{"enԃRM_^9{ގQ۽\7'eZK{c|kQ5j>~">IY>n>cBb]Gդu}HW#sn^e5ҺNW|EJ@/'v^+eUUX׫<ۦ6bpW g XIo#8le+z=8Nz^^L2sp nkei O̩?)I#Fh?'K=q~UD'TUuKtT:_Ưjd΍Ыg\Z8z~"zثDqkzA իg/;_ld΍ЫUߗ__ԫk^_e|uw* }؟SuEO7~w2e@8D:sa>< E{\YIf)4WφJxtcGD R?yQNy5٪q<]JӾY!޻?Mnnŏ*gK*&|[ڒO7yB[{t',֦ Gti~gx~PrQAg/eay,ZYQҵ95g??Y?y!?] i7i}Yw9jq>I*'u4kz#eX_X7Fz }vx6ЋEHzq`czq*ɌJvBl2q=}*dev#ɖ.{reRL/;{Z'zo& s}fޡ;ɧo8C_5LFG>i+ksʛT뜺rʳ9v#O:p$̕[ܙR*<] s |1xa8s(' xqL𜣆z`(m>yn6m!K^UE'=xE-D O[P7α*a'KwbKl Fm4j[oY`PpPnCj]ru`z z-ogz-[k5\㾴r_{I }Y[o6!6e*UZzIw#w,/ZcYQ\n$v;;ש- cIqXNW%'cXo|.?:9/*Ue!nYQ&/Qvww e+o¦2f<1{w* Yn\6s3o2svehFu^)+;7l )g΋sRT_v>sΞ~m(ݩ@&{#ۀOyYޚ+B:xse @]_}㶩{[}Fd=w]ƥs#+||D*/F9&'~>u]P<-).-[֮̆vmݯ6Se(wYm`cwUaG+5*j:}ρ*Ҁ2?]u rݯ7ӧo^>w^ppBmK~ Ϧñ"m: 3:b* wV`Mi4*yZPe{,ڡg1.#|eǀuv "F"MR^ U.w6y}+d\٩%g[͸d'68ԃtܫ,ݩ:{_A؇RK%̳rZ:XzRЯ3!i;)ix9iA+lZ}KEB9Kj;& Njɾ`Y2}An`K/UEOCi7,F3'/?ni,{_P72bv"ӗvXedB*}5̞//7^HjgL'cgR!v&δ)ޗ3;)Zе4~3NcpݥJ&'/J szo0 /:y8}Xl7R Y5X2; kmBYjer$?a#(gyxF!1yԥpg: ʍW>8oBiCB6λ_)O!?<_`l_,W3~ 'Ϡ0S*;RX~%{=i @Gyg|s$2e/y̛93n8!FoS8k<MBgXc81]@䓦apֲaP0MЙA%%hֲҳ˛ov.T6}]etsfAu2ab b0ʘab_F{|~OC\>-' ICgY^c"=}gB.i5h'%h:vuJz Kfuk9-g4/.n<^'m?Ƀܳ~6ȃ`mۻ.}O'v{ANmU<.'0nv׼ )Sz}WUF1;2XiX 9g'8]sco;Ȣ_*Hُ7dBʌ}KY7d.Dsj>((* 1ɼ?,I8,\й:w@e72ߨN;[?SPK' W'dub+iJX7PЅՉ>}nUO'8ߏ^^bkwQߏ)޻oѣQ:6ЉpQ'RNd 3\9KZq;"{2/!XӜ]ӣjm[䞘}އǞ0)V`촃_ <^ߓ=}ԡ]b]u?lsuXwη~?L:+ʏ)T[VF; `X|Rmh;@ݣ}7?kް0FL"{D 4 ~?޼=t+ih .빂O->ywvp7JjoO?P-_p w=]H~%8;k۬oޚS۬q{zU۬6f0gɱ#Ӏ^ԩE/9~cid~u|/"1o{,s'hg"6%L'^Zԁ,;lX/LNU{$~}I#T(Oݟ n!RUzqOC. O1"cpk>ae7BG&#ny#d6'ƥߙ9}ߡdN;ylwOӧDȴ]߱4B2‘Kk\S/ODט?5,tߢkl= JUWדQp|}5*EDnOʬhZ~^vN_rSc=yZ_im j`7mH,!:PN}k T:_PwCHk'h^|)2(eo4Oy.{&:l.ކcOnU?ٳ)Yyp>ŨmR֮x2.97,/ Dܬ-2p'bp c  R|C@ij#G{qdK-;MˠIvgI}'m},7ݩu}`^:/ ;KH1>O 95M% )X{K* R  ]cpum?@_;:)^Ӕ6߭E)/H+jw7\g7{Js גn9~ D~u_$?{RJ3yu/Y}C>zryf>c?,LoPخ CYS4y ω+5 ϓhx^c5_׍IT^e?,>)x]1S7#;0RjSGeڛ%A'𷆘j߾c=1}#nO%y N\PO3sߨj+-: ( e2iESh"(?ç<_E{\K9KA;U&6)McmTY?|O__+LJsw^èÿ@kl eׂ?;>KfߩZ> } 2Sf1}rJ($fC>S[5̇[ FȇznK}z}&Zp:k wqUr!^ [Wgk^S-6KGP'6KWVxy|&LB;X¿3B~Ea- }w ,>CW L_օ9El&ɮl/^]&!?M ,l{p=#yz|X˖;#fpB_`AggՑwa{?c)Xg}R439 b7} s՗hh2{E+#{E{z\'6eى1yߕ'MM/;FUF_<98N<^kxɓ{%];jm:wޮu}]ѧu+cpEB7}ʆ }?<_[~2V#뢌c\cgE\Q/\O.brglS^ʻº( &oMFp];a)yw|obB,M̘ ߹BXWߌFt+^:*Ꮺ߅2ʟ"7#4ʼZ 5ɖ5Y|Ϋ Wۧ|Bאon܏^.:YRdo%w4ߤG!!Z?/%ihoZ4Rve[v"=3EzF|* /Bz ZڷvDc Uo!_!LGd?TrB hG#WXwPg>@{ȇu$eHEQTedF=VQp̉>k^\2-~r2ir_淐yE藑 z绨oP[ٗV}d[}Oλj3X]UH;`JqDCi-?.Gn1;HMb$Է]~7aᠲL#dj-Cd#N?P5d#FwǦ~, עd/w oh/=}i0.1N&zssz^?kMIVHW^Hdyj3#9k"{3 gY3֪g% }ZlD:Iۋ{8zVhW`h E27_!l-UfE[skWژ6^>eeڟھuʣ]Ə_8~h_,NÖfymB?N+V֨Ne*ʋʞOp} vBmWOe_ik8 c b3aהMMߐک35Yw*>7pA8=1ǖ7Y.i-|+ aXʍb*ǨxJ}Kyz (#}Z4Q̄MyURyz%J*Kko,xc*p-μɣbo2'ְܨqߧS| +.g%>HiF;_ɇ-}"쐂mdb-E M5ފwJe,@ z)ThOi? 34+QۡV҈@,SGЇu µ'mXX.7QGտծ@LAjpʐXBxˌJuΪBimQڿGeWXC'Nk=Uu=-M}GֶTۏev  ::{t rl9ܣs7\wEu$G]i:]:C//sZ:ʛ{x|_:6ж~ږ~_=걾찈v^;sjl[xLVSys p1BzqnCx\ mCbp4>KGc%.y3Os@eEUZ)5ƖjWk{mCMB}4yƩ+!6WҴ}ؗˉ SXXh<0&qE<Ֆ9])ЅʻH1Pe|u{mRf_˾Pku֟)+.|A#98iE\=5R_~qJ6M =ʜ2gqZ3DkBEE=>CnyG#C p ȣܺvoYW(8>\|:~iG':?^K GP/~Wy1V$3*ؕE7iUE~ _݌#<ӭ{xQN+5;V?UηA}YW 7])\6Vҕ9E6=%w>[+F+D ?|q}}/ue̞Hޅ?I(ԕ ȮiUzt3wAtnΚ5..|9B>Qw+qwgﺟY }-ڧ*Dp}![gApէ̹zzG'9 f٢W٢30]QU(.˶FeTF' llb@l#$ʰ&m.WC lhR>Y[V5Db~Jn/.,,{36 Ñòàâèòñÿ çàäà÷à ðàñïîçíàòü M çàäàííûõ ñèãíàëîâ è îòíåñòè â îáúåäèíåííûé 1  M -é êëàññ âñå íåèçâåñòíûå ñèãíàëû. Òðåáóåòñÿ îï- òèìèçèðîâàòü ðåøåíèå çàäà÷è ïî âåêòîðíîìó êðèòåðèþ   , , , , п p V e K K K K K   , (1) ãäå e K – ïîêàçàòåëü ýôôåêòèâíîñòè, õàðàêòåðèçóþùèé êà÷åñòâî ðàñ- ïîçíàâàíèÿ ñèãíàëîâ â ðàìêàõ ñôîðìóëèðîâàííîé çàäà÷è; V K – ïîêà- çàòåëü îáúåìà êðèòè÷åñêîé îáëàñòè îòêëîíåíèÿ ãèïîòåçû î ñèãíàëàõ èç ( 1  M ) - ãî êëàññà, ó÷èòûâàþùèé ñïåöèôèêó ïîâûøåííîé àïðèîðíîé íåîïðåäåëåííîñòè; р K – ïîêàçàòåëü çàòðàò íà ðåàëèçàöèþ óñòðîéñòâ ðàñïîçíàâàíèÿ ñðåäñòâàìè âû÷èñëèòåëüíîé òåõíèêè; п K – ïîêàçàòåëü çàòðàò íà ïðîåêòèðîâàíèå óñòðîéñòâ ðàñïîçíàâàíèÿ. 2. Îñíîâíûå ýòàïû ðåøåíèÿ ìíîãîêðèòåðèàëüíîé çàäà÷è ðàñïîçíàâàíèÿ ñèãíàëîâ Ïîñòàâëåííàÿ çàäà÷à – ÷àñòíûé ñëó÷àé ìíîãîêðèòåðèàëüíîé çàäà÷è ìíîãîàëüòåðíàòèâíîãî îáíàðóæåíèÿ ñèãíàëîâ [5].  ñîîòâåòñòâèè ñ ìåòîäîëîãèåé ðåøåíèÿ òàêîé çàäà÷è íà ïåðâîì ýòàïå íåîáõîäèìî ïîëó- ÷èòü ðåøåíèÿ, îïòèìàëüíûå Ïàðåòî ïðè ó÷åòå ñîêðàùåííîé ñîâîêóïíî- ñòè ïîêàçàòåëåé êà÷åñòâà. Íà âòîðîì ýòàïå ñëåäóåò íà îñíîâå ýòîãî ðåøåíèÿ ïîëó÷èòü ðåøåíèÿ, ñëàáî îïòèìàëüíûå Ïàðåòî ïðè ó÷åòå âñåé ñîâîêóïíîñòè ïîêàçàòåëåé. Ñòðóêòóðà óñòðîéñòâà ðàñïîçíàâàíèÿ ñèãíàëîâ, ñèíòåçèðîâàííîãî ñ ó÷åòîì ïîêàçàòåëåé e K è V K , îïðåäåëÿåòñÿ ðåøàþùèì ïðàâèëîì [5]:              l l l l i H N P H   , / max : , (2à) . , , 1 , , / , / i i M l H N P H N P l l l i i i                              , (2á) M l H N P H l l l l M , 1 , , / max : 1                  , (2â) ãäå   – ñòàòèñòèêà, ïî êîòîðîé ïðèíèìàåòñÿ ðåøåíèå; l   – îöåíêè ïàðàìåòðîâ ðàñïðåäåëåíèé, ïîëó÷åííûå ïî îáó÷àþùèì âûáîðêàì çà- äàííûõ ñèãíàëîâ;  – íåêîòîðîå ïîðîãîâîå çíà÷åíèå, îïðåäåëÿåìîå èç óñëîâèÿ îáåñïå÷åíèÿ çàäàííîãî êà÷åñòâà ðàñïîçíàâàíèÿ Ì-ñèãíàëîâ ïðè íàëè÷èè êëàññà íåèçâåñòíûõ ñèãíàëîâ. 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Á. ÑÂÈÐÜ, À.Â. ÊËÈÌÅÍÊÎ ×ÈÑËÅÍÍÎÅ ÌÎÄÅËÈÐÎÂÀÍÈÅ ÝËÅÊÒÐÎÃÅÍÅÐÈÐÎÂÀÍÍÛÕ ÕÅÌÈËÞÌÈÍÅÑÖÅÍÒÍÛÕ ÏÐÎÖÅÑÑΠ ÊÀÍÀËÅ Ñ ÄÂÓÌß ÌÈÊÐÎÏÎËÎÑÊÀÌÈ- ÝËÅÊÒÐÎÄÀÌÈ Îïèñûâàåòñÿ ïðèìåíåíèå ìåòîäà ïåðåìåííûõ íàïðàâëåíèé äëÿ ðåøåíèÿ çàäà÷è êîíâåêòèâíî-äèôôóçèîííîãî ïåðåíîñà âå- ùåñòâà â êàíàëå ñ äâóìÿ íåïîäâèæíûìè ìèêðîïîëîñêàìè-ýëåêò- ðîäàìè. Èñïîëüçóåòñÿ íåðàâíîìåðíàÿ ñåòêà ïî ïðîñòðàíñòâåí- íûì êîîðäèíàòàì è âðåìåíè äëÿ ÷èñëåííîãî ìîäåëèðîâàíèÿ ýëåêòðîãåíåðèðîâàííîé õåìèëþìèíåñöåíöèè (ÝÕË) â òå÷åíèå íåñòàöèîíàðíîãî ýëåêòðîëèçà, êîãäà íà êàæäîé èç ìèêðîïîëîñîê ãåíåðèðóþòñÿ ïðîòèâîïîëîæíî çàðÿæåííûå ÷àñòèöû, à â êàíàëå ñîçäàíû óñëîâèÿ ëàìèíàðíîãî ïîòîêà. Ââåäåíèå Òåîðèÿ äâîéíûõ ýëåêòðîäîâ õîðîøî ïðåäñòàâëåíà äëÿ ìàêðîýëåêò- ðîäîâ â ñòàòüÿõ [1-6], ãäå äèôôóçèÿ â íàïðàâëåíèè ïîòîêà ïîëíîñòüþ èñêëþ÷åíà. Íåêîòîðûå èç ïîñëåäíèõ ïóáëèêàöèé [7, 8] ïîñâÿùåíû ìèêðîïîëîñêàì-ýëåêòðîäàì â êàíàëå, ãäå îñåâàÿ äèôôóçèÿ ìîæåò áûòü çíà÷èòåëüíîé è äîìèíàíòíîé ïðè ìàëûõ ñêîðîñòÿõ ïîòîêà. Àëäåí è Êîìïòîí [10-14] ïðåäëîæèëè èñïîëüçîâàòü ìíîãîñåòî÷íûé ìåòîä, êàê àëüòåðíàòèâó ñèëüíîíåÿâíîìó ìåòîäó [15], äëÿ ýôôåêòèâíîãî è ñòà- áèëüíîãî ðåøåíèÿ ñòàöèîíàðíîé êîíâåêòèâíî-äèôôóçèîííîé çàäà÷è [16, 17], ãäå ïåðâàÿ ìèêðîïîëîñêà â êàíàëå – âûøå ïî ïîòîêó – ÿâëÿåòñÿ “ ãåíåðàòîðîì ” , à âòîðàÿ – íèæå ïî ïîòîêó – “ äåòåêòîðîì ” . Ñîîòíîøåíèå ìåæäó òîêîì äåòåêòîðà è ãåíåðàòîðà îïðåäåëÿëî ýôôåê- òèâíîñòü âû÷èñëåíèé â ðàáîòàõ ýòèõ àâòîðîâ.  äàííîé ñòàòüå ìû îïèñûâàåì ÷èñëåííîå ðåøåíèå çàäà÷è êîíâåê- òèâíî-äèôôóçèîííîãî ïåðåíîñà âåùåñòâà â êàíàëå ñ äâóìÿ íåïîäâèæ- íûìè ìèêðîïîëîñêàìè-ýëåêòðîäàìè äëÿ èññëåäîâàíèÿ ÝÕË ïðîöåññîâ â òå÷åíèå íåñòàöèîíàðíîãî ýëåêòðîëèçà, êîãäà íà êàæäîé èç ìèêðîïî- ëîñîê ãåíåðèðóþòñÿ ïðîòèâîïîëîæíî çàðÿæåííûå ÷àñòèöû, à â êàíàëå ñîçäàíû óñëîâèÿ ëàìèíàðíîãî ïîòîêà. 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Ñõåìà ðåàêöèé äëÿ îïèñûâàåìîé ìîäåëè âûãëÿäèò ñëåäó- þùèì îáðàçîì: , A e A g    (ïåðâûé ýëåêòðîä) (1) B A 1 k     , A e A g    (âòîðîé ýëåêòðîä) (2) C A 2 k     , A A A A g * 1 bi k         (3) . A A g ECL f k * 1      (4)  ïðîöåññå ýëåêòðîäíûõ ðåàêöèé (1), (2) ïðîèñõîäèò îáðàçîâàíèå èç èñõîäíîãî âåùåñòâà g A ïðîòèâîïîëîæíî çàðÿæåííûõ ÷àñòèö – êàòèîí- ðàäèêàëîâ  A – âáëèçè ïîâåðõíîñòè ïåðâîé ìèêðîïîëîñêè-ýëåêòðîäà, è àíèîí-ðàäèêàëîâ  A íà âòîðîé ìèêðîïîëîñêå (ðèñóíîê). Ðåàêöèÿ ðåêîìáèíàöèè îáðàçîâàâøèõñÿ ÷àñòèö (3) ïðåäñòàâëÿåò ñîáîé ðîæäåíèå ñèíãëåò-âîçáóæäåííûõ ñîñòîÿíèé * 1 A , êîòîðûå ÿâëÿþòñÿ ýìèòòåðàìè ÝÕË.  õîäå ìîíîìîëåêóëÿðíîé ðåàêöèè (4) ïðîèñõîäèò èñïóñêàíèå êâàíòîâ ÝÕË ECL  . 2h 0 0 w y z x L 1 L поток y = d L 2 L 3 Íà ðèñóíêå ïðåäñòàâëåíà ñèñòåìà êîîðäèíàò äëÿ êàíàëà ñ íàïðàâëåí- íûì ïîòîêîì è ñ äâóìÿ ìèêðîïîëîñêàìè-ýëåêòðîäàìè. Ñ÷èòàåì, ÷òî â ðàñòâîðå ñîäåðæèòñÿ äîñòàòî÷íîå êîëè÷åñòâî ýëåêòðîëèòà äëÿ òîãî, ÷òîáû íèâåëèðîâàòü ïðîöåññû ìèãðàöèè. À òàêæå, ÷òî w – øèðèíà ýëåêòðîäîâ çíà÷èòåëüíî áîëüøå, ÷åì èõ äëèíà, ò.å. w>> 1 e x è w>> 2 e x , ãäå 2 3 2 e 1 1 e L L x , L L x     , ÷òî ïîçâîëÿåò èñêëþ÷èòü êîîðäèíàòó z êàê íåñóùåñòâåííóþ. Òàêèì îáðàçîì, íàøè âû÷èñëåíèÿ ïðåäñòàâëÿþò ñîáîé ðåøåíèå äâóõìåðíîé çàäà÷è. Ïîòîê íàïðàâëåí òàê, êàê ïîêàçàíî íà ðèñóíêå. Ï xklU[naZ n[%E4 E`AQ DAӊ "bQVI!4F#EE@H oAP>#Yww& cNy=wvi@IMzPQ? 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dV6Jˮ'z|Dvkd} f+$V\7-xO.mX,, 43 Ìàòåìàòè÷åñêàÿ ìîäåëü óðàâíåíèé (1)-(4) ïðåäñòàâëÿåò ñîáîé ñèñòåìó íåëèíåéíûõ äèôôåðåíöèàëüíûõ óðàâíåíèé â ÷àñòíûõ ïðîèçâîäíûõ:                                C C k C x C V y C x C D t C bi x 2 2 2 2 ; (5)                                C C k C x C V y C x C D t C bi x 2 2 2 2 ; (6)                          C C k C x C V y C x C D t C bi * * * x 2 * 2 2 * 2 * * , (7) ãäå * C , C , C   – êîíöåíòðàöèè ÷àñòèö * A , A , A   ñîîòâåòñòâåííî; * D , D , D   – êîýôôèöèåíòû äèôôóçèè ÷àñòèö * A , A , A   ; bi k – êîíñòàíòà ñêîðîñòè áèìîëåêóëÿðíîé ðåàêöèè (3); x V – ñêîðîñòü ïîòî- êà æèäêîñòè â êàíàëå âäîëü êîîðäèíàòû õ;  – êîýôôèöèåíò êâàíòî- âîãî ôëóîðåñöåíòíîãî âûõîäà; * , ,      – âðåìÿ æèçíè ÷àñòèö * A , A , A   ñîîòâåòñòâåííî. 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(8) Íà÷àëüíûå è ãðàíè÷íûå óñëîâèÿ äëÿ ñèñòåìû óðàâíåíèé (5)-(7) ñëåäóþùèå:       0 0 , y , x C 0 , y , x C 0 , y , x C 0 y x все 0 t *        ,       0 y t , 0 , x C y t , 0 , x C y t , 0 , x C 0 y L x 0 t *                  ,       0 t , 0 , x C t , 0 , x C ; C t , 0 , x C L x L * 0 1        ,       0 t , 0 , x C ; 0 y t , 0 , x C y t , 0 , x C L x L * 2 1            ,       0 t , 0 , x C ; C t , 0 , x C ; 0 t , 0 , x C L x L * 0 3 2        , (9)       0 t , 0 , x C ; 0 y t , 0 , x C y t , 0 , x C L x * 3           ,       0 y t , h 2 , x C y t , h 2 , x C y t , h 2 , x C h 2 y x все *             ,       0 t , y , x C t , y , x C t , y , x C y все x *        ; çäåñü Ñ 0 – íà÷àëüíàÿ êîíöåíòðàöèÿ ðàñòâîðà ýëåêòðîëèòà. Ìãíîâåííûå òîêè íà ïåðâîì è âòîðîì ýëåêòðîäàõ ìû íàõîäèëè èç ñëåäóþùèõ ñîîòíîøåíèé:                         1 L L 0 y 0 y up dx y C D y C D nFw ) t ( i , (10)                         3 L 2 L 0 y 0 y down dx y C D y C D nFw ) t ( i , (11) ãäå F – êîíñòàíòà Ôàðàäåÿ; n – êîëè÷åñòâî ýëåêòðîíîâ, ó÷àñòâóþùèõ â ýëåêòðîäíîé ðåàêöèè (1) è (2). Ìãíîâåííóþ èíòåíñèâíîñòü ÝÕË [20] îïðåäåëÿëè êàê     dxdy t , y , x C w N t I h 2 0 * ECL A ECL        , (12) ãäå ECL  – ýôôåêòèâíîñòü ÝÕË, êîòîðàÿ ñîîòâåòñòâóåò âûáðàííîìó îðãàíîëþìèíîôîðó; N A – ÷èñëî Àâîãàäðî. 6xlVǟ(-}O -`Rqa" V&2&Sd9hHf R2l)q !DvЩ[uۻp}pvs{|sm7"]+"cD>/a E/a"hmy;j"_~6˻=.ܓ^y$'5Ŏ9vɖ%XŒ#~y=O[|iVKl;jr2}oH\c2ϕKhoEFI> )JyB?mߏTz;fWuv/[nb ˱o`K1B e'h/=glj7qD5`/}Ow+Y_# meE2+x51Abr/~WV9:`M`\yⴹ119{w?Fjh7XoL˕Zx {մF.Q{/E|IcLm]0cYjr^ /xNL|'dx"ɻ5rr;1JtΕs"\ xH4uɃ`}x9w;]opo즏> -`}?ʕ"'8oʱ^%\{:5  ]bG[Byso3ث=~_ pv`oo7\?Y|SiOk]Z3q]^`]<0Kd [wU<[ng[g%,w.ϐ@^y75_=5~R~~\A Lxݧtmݴ_gcuS{ױRg6u.&ܽR߃_ `9Eؓby֟,%r0\Wf ;u>~Sz3ݽ1YJcpگay~޵fۻ ;[S?{Dz1k ~|әbkhfi1+`IGo1|=^ 3Izw 7{ :._I_%RHΞusUyZ?{h+jt[$#ԟ+i|śd?I3^- cywRdl#PKzYSe V|8ﵸ?1Nuƻlj9ǽvcY,"v>v*L?bn[/Oޯ R!q8옎2fÉb%+eWa{|؏Rb%ϫ.0bhq=Ř/Kwi(mS Ͻְ3z`}`m+ܶb35N]_ȚV.zt.x-&{妯u9[#VQ'pm(H1Ը}`r~WN=?Q~=Zm\ӳg5X)ߌ%cUuҊٶQ2҂׺k];(sඓq C\o`½91pq2q|:N_|KǙN/Gqt^}qܸM?8g5D@06.]r3zΠXOq?[bW '[:-~߱H2XN;(+%ޕ-A* H[ Ş\Wu\ C~y@ֆ1!?s9OQ/S&c˹$ׂ͗}hIn \K*~y: LI70,EA]H>/Cc*.yPW&=RI}* ^ÞzTB ׆`(]&w&ܿuƒ]~D-KIճjZ9W0nɍ'ibb6m˴mT_BBBBBaࢉ*CB%Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:24  0| lD  7 | (| (16 2 / 6| 1 8 {DxVUE )o>܀Q$濑+Q^fNAEdXdIf֨3Sk2oNޱ+du叠^ ><9{kih;Dѷn?j=7^E<=ɿF շ)pKE9~aMiaM8f=7FWEEWDWG%'kZh-ߢ;T0D.uKbA0]ʩ fHs?U[sH(t+tȃCTPFPl󦯃ˎ;4Mi1-ljѯt"GӺxNTR+Uv8QzmNkh[n:'̋ѱ#C6y`鰙1^4Ό>xY|{nH-V_R|`̘6 }م]q<\i π뛚VLW4R\}OiEtiƦ}[۶Ѥt mft͈8#ye+һSᳮ=sZ$?)uA1W*<&]1, d~çG92J($<+?ҜM6OW\qTud?XX6\xvCSPl'Id31Mbe/65lNU\lD#&1}×lBo㕗)a3bbaIݓ oSYH6gnymFk-wDhcLB\%&C'drL4O ibGGUd{E3McO/T 'uY&6<^oQ*$FC2M-75 OvoȜη|:L6J|M^S\+:7ߠw%Z{&Q ^x*;Le.{CI;:/hؠGDhr%Q;J)z^7nZlQXDk/ -+*'弴hC-i` =i}x{WZsg`CD7xE~ k"_GVO?qDb/ <`.+uTW$|C~"M2^ 1+{1tՕRI[m re & wh^ZQ}^xb*8xwV x(yIl;l~bioЀ\ݢ =fT|K37:#sf[z.FG9g g!Mܣ9M2Z0"M|ѷ]67\-7XAa!]:C+(?iuu,o;dPcEd?Kg̕E׃ʇeu輸ZѦIX/Y&RҸC R^v^Vg--oѸ7l{E{zѐy/lvڱ'+ۣKa$U!םlaq5-?F7{ _ $*xݶmÛN7a>=9]JB=Z:kH6Ǿ2'IN[bayTxiNnwa49:[FgFE < W˃p+jOQ|j;9/ϑiX6 c^wcNb‰/nn[ncO5|ߗ TwCU|\6[o6{ QypbM8ka^ɷT\̓/犯\EPKe?|.[ gɓ>׃6_?4`@ fH#ܽǭ-I-nǘjĸ.iqXN)"j=-P5r>kX7PRYlm^2ὥ_};@f`OVL?Ieʵ劣Q&1mΔTRu!۸MgK`-Әc(Ǘ>giH &q@ãTIq}` "y7Ba}/J:9߆ ^ڐFoO:ې^ڐq16u5z*NI~crpG>pxyEZrf8|պKu.g{E^-ph|G~7H4gIvkϼ{HvwX Y/{֘XvCW@ MUӒ`ɧ_wkk5 "%y/D">9w&g:jd{5a 9fk3'WfަO!&R3<|N8l2_sக:ۋ}W]7_kZsσ3F ͮ=mq-Kw ,bl<|䎁!v"g$R{mп+' ^Oy[裖fL ݁1UQY:nk )Go¡'ԮW}i{e?NSD1mhofנOT55q O oMWy|sv=G#oo@goh$ʼngo\(LJÚcwL]Uz|VNKG#p=Wkѫ#-f-z U>ˣi|W_sUgjI:ɠ@ $%CB|Ϸ,jo2Iv ^v‰f/xAWh$+抗Ư +V㒮xwty]켰s$/+`]a⬮@0UuCK ]Su_7^WI0|tF|h^?BK]{W2~u;~X. euN ~o˾`\e$-]F:EgZu[ԹRW_㿿tφMm|>I-<)<(JZYl$zm]aQJ_G6ѿKPv#bK6o:*H#i @YqV}}_a)16ȚkR/bt "*ޮz[b',ρZ'o{<4>~!̀Fb˯YOt$t1Mhձn=7ǃe<4G^w}XW`g6.Cƞ[dpa]'o>{wLD{LΑlRL\ pp&ɞq&[_v&NSa*OQR@[p)gZZ6+=@zX$tf~̝:CO`= rohimhgx~zطriG0R,<ĺrL6vڰt?j@包zlAt2#׾_uQߝ|yQyheuw많ޖ5._]7ì<_דtjŐN]'TgXٶa,!bOb$=^ }z*+=%>OA#CqpvpKܻ% ;PY T adj{C:Bpv=yN=&|!8ZpE~94<8[[C]w3E?,%`CyN]1X}5"s1Rͣlj|s1|5"^]Hϊ)=$K|Ҷsκ:斾ͅy2#n ĸ.WH;N4jmQ,/H.~upK MppaO~ZJ_{t0$֭~qBzQ5Cpp#>p2b!rC8esFLyZJk-i}Ca|-gs," m,ɁIj0Q{i_/ _,,/Y, 7!^nWm.gh|S<\Xòq.CpȪ%C_փe/|/}|k2mRpl'_mM|Kxﵚo|NټlimC4P`|iEW1뽊*fo5_/u/eȣ5U'*hyRU_ڡ.W[GcN9CS)OkKme1Ek]h_vܨ [37<"g| u2<ڝ|U7Xe˰Vg}>Jd,oܨ} ymWoe`C|+ySJnoe@^1 Ŵ\|wWx‰3TdpjEй~-7@0!|d}4XlϪͣ?j !~7M:y}E\{9٤5=_.s S }߭"OE'l5O~v~-erxZW*WWovT!?0i(Smu0o[YVJloJ|mEVTߤZDM3g[Ao[s!wSˣo[5Gf[};am+xXj߽{~[_}+[_cUd{ mflb囆u5c隋󿃜k.fb^0~5`(:k!8BpQlkfWl:Qcg򙳟J|5![(Z䳈noE}nM;[@oO|B$^>3;$'eIeל}N|3)JZZž־sqgwhe|5IhxT^~YOkWuA|DxZDv:.6فff0<⬍K6.Eޟ.(׾Xg#;K 7m(XٷS*. k~諢2}v=egiJ6voH~oĽåi} VzuPMZ}n6GzطoG[eMqOl~ĞS MU:?{Q=Fs5כywB:2egqwq=Nw$s p=zA" \h|Y^ 9[),! }7_S@^OG?ڬEO/bWaˮ{7[3_ ܼn#?>}Gi)Wٚ}BpeYY왯jb!8 \g?+=V{Pymd=]<<-v%\mBsU^"wy ?q;#/~Ǎv]e-ϒH+zXU~̻dh`.ǫOL/ȁI/\G_~;]۵6~ j~!|Uwsh]}&KC3,{""Pam cQX &4kڬIe&_=2|!~MW݆}<+Ed\mn8C' G]~͇4mђi!ӆ}ͯ9 C72fQ14њ$>']n+`.֙6C@ ݢ;L;*f<:볃=[?#So禲 lmmvQ%lGi"zՆ3_|ɋD=ɻGw垓-\,Zw0@p<{3p70NpZ:'lXqJs@{/s>l9_E&Ss?UTV~X;3Kw!+Ͼ ,_3u,k` mrEK؋vFf a_$C΋GW#Հk{Iwuj[02c_Syu~.7!gi Dg`Gۑ{٦ Ŏ4=l(miQ4С^9D8R Z4x|>V1u_fMU8c|˄[aa]I*;Y!?QVY|/m5*ڂxV1v3K}=H=.=6z|l=fĔ8b(gPR:kC;c8kyßal֧lES¿+S]l`C[]׊/foUC- +I~OnO^Tk8oL r`r97?" 4b~bҔc{/ʱ W먏Wov40VO{;ex6>9pI2kpxIG)_V?.W~!ꏱ5GޘGugeQc>I~"Edgde-1]ItMrk?hG{'eg׺8W܌PotIevĆGS]&= |}IeBuwhGء͗1N<:So0Sgt (3]ה/u۬o+VQ yޭi_A>} ~=[$ũ2. AR7 v- 녏qC??9A #y`񚶔N ( $OF_bO+NEKTxe^2phxֈĔ\Ț6~l6n3Gd5gOCa%Y!ОУ-֫F[ߨ0[Uy[C*qze| Ҍq1k{:UW\cm%|wbB.5;oɁ[zoϓ~<"-TH17M 4 :K:(IfG f\m͍:mhǪ>Ok)l!WNϤ=c'W?{|{K w$0ċC}}] '^i'S @"7G '/JFwzA yx)Ɨ o]_h|:=?xw2 !VŎdC!NE|BU;yb5OZSދ@orF}y|T"{6w߳]3v~Bo_g8t0u㋮]1wߩ M2sS嵝0܉߻5Ygn/0I/Ӗ˽ &l2 M(ĴVמs-2Zٞ}{y5:wӵMm}kZw(n:w6 }Eos<v+ |\ T礖c#AAN9_4kOfL,) ytxZ/ue݆h ~72y7Bym?׉}u(-srƪ ^Q|!?$ &ʖ6{EƷjMQI/oCAgC j ᫴z*Iφ*K^%t>$Cl})3 w(oq}%>h`Hmv}vw+ |\ -q`|)[G/zUx7W'uZR f 8'̗h:]Jiڱ/1e{A98㼵~h+w{ bp6X9ȏls闼]j'ɔ2%Βe:xK1;Kc4I+Nm:ق5%q,j?.Iウz*_ @kUe[$o_z2R~p3TdoNgN#y3T>{@o_t5Wm Gb|8 wѯ 2Xhuj";>~w?}z 3uʋke u uPjM-|-3a\z/^bΐSY}0:3ZL(8WZۅ_ggmC[=th޵̹~YK0v~Ư:4}N|,sbnW8:oIm%6"Y:lnZ |\SUvxK.P|eNlr=ɆH18lTʴ8x#xy>O2(cn CA 'U>T !nU83eQѺ3gX=Լ?1 4x?<Ćgsw+Lz+:I\}OiV8=6ڶo&cm3oFtMIL%kGpY$~Ϣ)S5G_ˆ)S㴬Vb\%,}UoXM,=1bed9_YVY\EbdSZIw%YܝJ?%o#/"uO!/{*g<j,,z 45 Ðàñ÷åòíàÿ îáëàñòü Îáëàñòü ÷èñëåííûõ ðåøåíèé ïî êîîðäèíàòàì õ è ó ñëåäóþùàÿ: 1)           h 2 DT 5 если h 2 , h 2 DT 5 если DT 5 y , y y 0 e e e max max 2) 2 2 e gap gap 1 e 1 x x 2 x x 2 x x x        , ãäå 1 x – ïðîòÿæ¸ííîñòü îáëàñòè ïåðåä ïåðâûì ýëåêòðîäîì; gap x – äëèíà ùåëè ìåæäó äâóìÿ ýëåêòðîäàìè ( 1 2 gap L L x   ); 2 x – ïðîòÿ- æ¸ííîñòü îáëàñòè ïîñëå âòîðîãî ýëåêòðîäà. Îñíîâíûå èñïîëüçóåìûå â ïðîöåññå ìîäåëèðîâàíèÿ ñîîòíîøåíèÿ:             e e e max e e e e max e e max 1 x 5 . 0 DT T V если , x 5 . 0 x 5 . 0 DT T V если , DT T V L x ; e e max 2 DT T V x   ; ãäå   2 e 1 e e x , x max x  ;   * D , D , D max D    ;                     h y если h y h 1 V h y если , V V max 2 2 max 0 max 0 max ; 3) äëÿ îãðàíè÷åíèÿ ðàçìåðîâ âû÷èñëèòåëüíîé îáëàñòè ïðèìåíÿëîñü íåðàâåíñòâî 10 n где , x n DT T V e e e max    , ÷òî ïîçâîëÿåò îãðàíè÷èòü âûáèðàåìóþ ïîëüçîâàòåëåì äëèòåëüíîñòü ýëåêòðîëèçà ïðè ôèêñèðîâàííûõ îñòàëüíûõ ïàðàìåòðàõ, à ñëåäîâàòåëü- íî, îãðàíè÷èòü è ðàçìåðû ïðîñòðàíñòâåííîé îáëàñòè, êîòîðûå çàâèñÿò îò äëèòåëüíîñòè ýëåêòðîëèçà. Íåðàâíîìåðíàÿ ñåòêà ïî âñåì êîîðäèíàòàì Ïðåîáðàçîâàíèå êîîðäèíàò ïî êîîðäèíàòå õ                 arctanh x x ; x x tanh , (13) çäåñü  – ðåãóëèðóåìûé êîýôôèöèåíò ñæàòèÿ ñåòêè, gap e x x 2 x    . 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Ýòè ïðåîáðàçîâàíèÿ ïðåäëîæèë Ôåëüäáåðã [24]. Ìû èõ èñïîëüçóåì äëÿ ýêñïîíåíöèàëüíîãî ðàñøèðåíèÿ ñåòêè ïî êîîðäèíà- òàì õ è t. Çíà÷åíèÿ ãåîìåòðè÷åñêèõ ïàðàìåòðîâ â íîâûõ êîîðäèíàòàõ èìåþò âèä ; x L tanh L ; x L tanh L ; x L tanh L 2 2 2 1 1 1                                                     x L tanh L 3 3 3 ;       1 ln max . Ìàòåìàòè÷åñêàÿ ìîäåëü â ïðåîáðàçîâàííûõ êîîðäèíàòàõ Ïðîèçâîäíàÿ ïî âðåìåíè (t) â ñîîòâåòñòâèè ñ (22):                e T dt d t e , (16) ïî êîîðäèíàòå õ â ñîîòâåòñòâèè ñ (20):                   2 1 x dx d x (17) è                                          2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 x 2 1 x dx d dx d x ; (18) ïî êîîðäèíàòå ó â ñîîòâåòñòâèè ñ (21):                                        2 2 2 2 max 2 2 2 2 2 2 2 2 e y dx d dx d y . (19) Ñèñòåìà äèôôåðåíöèàëüíûõ óðàâíåíèé (5)-(7) â ïðåîáðàçîâàííûõ êîîðäèíàòàõ òåïåðü èìååò âèä                                           c 2 c 1 1 x D c e T 2 2 2 2 2 2 e                                             c c K c c V 1 x c c e y b 2 2 2 2 2 max 2 ; (20) 1x pUG}|$Dq*@ MÇδu4`iVP%jʗhZ-*LZ-HKP >λ暐pݳ{߳{ù!&ɏ|YY_-2:!9:ڃ[H?7xrqG2ZZ+9\=X^ĝLd-9|͐y ɑuvg,NG\I+7 * 7Jf^[( DwZ}'de<-5G ̭KDe!gY*ϓ{crBw$qr(/19˷Ir,//Cw'VVte!dIo|~A%p+H܅gdZ o5?6#c92qMhM';O$'K%`S$[us lrbȍ%?[9+1H~` k@WK7cϡE<ɖm" gar駲ߩQFW1fJgxV|~ 5NF99rzP&WASM΍wf_<K՟*v"@&R˞۳:9, gͬy19RcYΑJ {v;WJds4UօYDL!gr_`8C<4gJ wR)DX9!gl\V0V|͟8^ITM|Q7,*tʖܝӉWsr?2.'rshdrer3ɇLYΜާi\kQbXT{Zښ7ӌI743g:>ΖI;F.VPc{_O3\(KPl<ͽbplƽ^gUw¹w[sEf^=֚|:ZLh(1oB/+1e~7 p Y@D"$-X=3LzT*b|/߂݂_^ǽtpKJx_pו`>8Ë i [: y~:=`}1Йm+?mi36NzkMk}WA ӓƎRm=|״f?ets?v}mKaۻi?e~19g+FK[Կn@`K`-=ն \An"ÿ% gg1cPN4MDL|Lr`ݟ\{c!{戟 s|X~~DTywSz/IlD4=왾V^xѼQrX5cؙkڽiҶ}k ~ٻ﯍/y pg~ ]I{ꔋ[9/yb @)R \ڲ?crzƼp |d&vlVcj##;1GNoUo~՛=?>a9**>.@d'h8ir~ rsW0v)\#mߢECD~8,Qgώu2s~*9F(162/ T1@ Zn{hsx] VU0:*fx8*O$t,Ti*G7㑏$5&7f2ni{+#Bwa}o s=Z{sjC:Λ;w@)fwTM-S1'c]qB:UB<;9ޜ8؝qs:߃?ݹqj6 d8{?cu[5rq;\mt٥ߐsaӗ21f9\cX0.-nn; go[o׷USMz;sfڌF9ނ+ҥ\9H<;NykhPKO:lfI|7XiP+)xx;툔g-dn^_9Zȶyh}|ci{&_|H('}7ڗK(*l`u-G' U5 AwNq݇qu;ڽ]S`̄fU8= {l<}< f{G>r98_.n.SΟk7Lhڀ#8]?tݨpaMǛhI0F,|UbC/6e_O #)$hxA֬)_~syo_ȓHPخ 8)<8xY);^|{T;x /-"_BfX]0q~C-\_>{}Cخ0Ͷ3h/⯟@ ["MסλY}sܵM/3fe 4"|]8` SY|?ym<C!؀}a*o5-|L[ =M+yzШw_gk}8<nя73 վ>>j*<}){v~;OO1c\4/a[>ĆO;Ej/ Nob1*9af~<ɑl8]X8CB1X ߢc ! 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Âûâîäû Çàäà÷è êîíâåêòèâíî-äèôôóçèîííîãî ìàññîïåðåíîñà â êàíàëå ñ äâó- ìÿ ìèêðîïîëîñêàìè-ýëåêòðîäàìè â óñëîâèÿõ íåñòàöèîíàðíîãî ýëåêòðî- ëèçà ìîãóò áûòü óñïåøíî ðåøåíû ïðèìåíåíèåì ìåòîäà ïåðåìåííûõ íàïðàâëåíèé ñ èñïîëüçîâàíèåì íåðàâíîìåðíîé ñåòêè ïî âñåì íàïðàâëå- íèÿì. Âû÷èñëåííûå òîêè ñ èñïîëüçîâàíèåì íåðàâíîìåðíîé ñåòêè ïî âñåì êîîðäèíàòàì äëÿ çàäà÷è êàíàë ñ äâóìÿ ìèêðîïîëîñêàìè-ýëåêòðî- äàìè ìû ñðàâíèâàëè ñ íàøèìè íåäàâíèìè ðåøåíèÿìè äëÿ îäíîé ìèêðîïîëîñêè â êàíàëå [29]. Âû÷èñëåííûå òîêè, ïîëó÷åííûå â ïðî- ãðàììå äëÿ äâóõ ìèêðîïîëîñîê â êàíàëå, äàëè ïðåêðàñíóþ ñõîäèìîñòü ñ òîêàìè, ïîëó÷åííûìè â ïðîãðàììå ñ îäíîé ìèêðîïîëîñêîé â êàíàëå (òàáëèöà 2). Ñõîäèìîñòü ñîñòàâèëà ìåíåå ÷åì 0,1587%.  îáåèõ çàäà÷àõ ïðèìåíÿëèñü îäèíàêîâûå íåðàâíîìåðíûå ñåòêè ïî âñåì òðåì êîîðäè- íàòàì ñ ðåãóëèðóåìûìè ïàðàìåòðàìè ñæàòèÿ ñåòîê ïî êîîðäèíàòå õ (  = 1), ïî êîîðäèíàòå ó (  = 0.01) è ïî êîîðäèíàòå t (  = 10). Ñïèñîê ëèòåðàòóðû: 1. Braun R. J. Electroanal. Chem., 19 (1968) 23. 2 Matsuda H. J. Electroanal. Chem., 16 (1965) 153. 3. Aoki K. and Matsuda H. J.Electroanal. Chem., 94 (1978) 157. 4. Cook R.N., Phil D. Thesis, University of Oxford, 1973. 313ð. 5. Compton R.G. and Stearn G.M. J. Chem. Soc. Faraday Trans. 1, 84 (1988) 4349. 6. Compton R.G., Coles B.A. and Fisher A.C. J. Phys. Chem., 98 (1994) 2441. 7. Rees N.V., Dryfe R.A.W.,Cooper J.A., Coles B.A., Compton R.G. , Davies S.G. and McCarthy T.D. J. Phys. Chem., 99 (1995) 7096. 8. Rees N.V., Alden J.A., Dryfe R.A.W., Compton R.G. and Coles B.A. J. Phys. Chem., 99. 1995. 14813. 9. Alden J.A. and Compton R.G. J. Electroanal. Chem., 404. 1996. 27. 10. McCarthy G.J. Investigation into the Multigrid Code MGD1, Harwell Rep. AERE-R 10889, 1983. 11. Wesseling P. Multigrid Methods, Lecture Notes in Mathematics, no. 960, Springer-Verlag, Berlin, 1982. P.614. 12. Wesseling P. SIAM J. Sci. Stat. Comput., 3. 1982. 387p. 13. Bramble J.H. Multigrid Methods, Pitman Research Notes in Mathematics Series, no. 294. Longman, Harlow. 1993. 14. Paddon D.J. and Holstein H. Multigrid Methods for Integral and Differential Equations, Clarendon Press, Oxford, 1983. 15. Alden J.A. and Compton R.G. J. Electroanal. Chem., 415 (1996), 1. 16. Gerisher H., Mattes I. and Braun R. J. Electroanal. Chem., 10 (1965) Òàáëèöà 2 Âû÷èñëåííûå òîêè äëÿ çàäà÷: êàíàë ñ äâóìÿ ýëåêòðîäàìè-ìèêðîïîëîñêàìè è êàíàë ñ îäíèì ýëåêòðîäîì-ìèêðîïîëîñêîé Вычисленный ток, мкA Скорость потока f v , cм 3 с -1 Одна микропо- лоска Две микропо- лоски Ошибки сходимости, % 0,0005 0,37189 0,37242 0,1425 0,001 0,37199 0,37252 0,1425 0,005 0,37519 0,37575 0,1493 0,01 0,38429 0,38490 0,1587 (xLe{E{ B(HS ´Y*tBJS 5é䔲2[˵Z\˚Zd-r˿zλ+Wڲ?^wss<}LQ("bD Lq?VdAlTr6#V3.ҌwAKݔL={lkbs9{zHZ*?}ڛƂ~Hkl&Jr=L!}%Nz%"&ݺ҈Orul;y1 9bY+eleK"Wx84gd!7/⷇>"V.SK2lvl325bL]f$H9? 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Compton R.G., Coles B.A., Gooding J.j., Fisher A.C. and Cox T.I. J. Phys. Chem., 98 (1994) 2446. 18. Faulkner L.R., Tachikawa H., Bard A.J., J. Amer. Chem. Soc., no.3, 94 (1972) 691. 19. Tachikawa H., Bard A.J., J. Chem. Phys. Lett., no.2, 26 (1974) 246. 20. Áûõ À.È., Âàñèëüåâ Ð.Ô., Ðîæèöêèé Í.Í.// Èòîãè íàóêè è òåõíèêè. ÂÈÍÈÒÈ. Ñåð. Ðàäèàö. õèìèÿ. Ôîòîõèìèÿ. 1979. ¹2.135 ñ. 21. Levich G. Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962. 22. Lévêque M., Ann. Mines. Mem. Ser. 1928, 12/13, 201. 23. Pastore L., Magno F., Amatore C.A. J. Electroanal. Chem., 301, (1991), 1. 24. Feldberg S.W. J. Electroanal. Chem., 127, (1981),1. 25. Heinze J. and Störzbach M. Ber. Bunsenges. Phys. Chem., 90 (1986) 1043. 26. Heinze J. Electroanalysis, 124 (1981) 73. 27. Thomas L.H. Elliptic problems in linear difference equations over a network, Watson Sci. Comput. Lab. Rept., Columbia University, New York, 1949. 28. Bruce G.H., Peaceman D.W., Rachford H.H., Rice J.D. Trans. Am. Inst. Min. Engrs (Petrol Div.), 198 (1953) 79. 29. Ñâèðü È.Á., Êëèìåíêî À.Â., Êîìïòîí Ð.Ã. / Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. 2000. ¹ 2. Ñ. 24. Ïîñòóïèëà â ðåäêîëëåãèþ 12.08.2000 Ñâèðü Èðèíà Áîðèñîâíà, êàíä. ôèç.-ìàò. íàóê, çàâåäóþùèé ëàáî- ðàòîðèåé ìàòåìàòè÷åñêîãî è êîìïüþòåðíîãî ìîäåëèðîâàíèÿ, äîê- òîðàíò êàôåäðû áèîìåäèöèíñêîé ýëåêòðîíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: ÷èñëåííîå ìîäåëèðîâàíèå ýëåêòðîõèìè÷åñêèõ ïðîöåñ- ñîâ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-64. Êëèìåíêî Àëåêñåé Âèêòîðîâè÷, ñòóäåíò ãð.ÏÌ-96-1 ô-òà ïðè- êëàäíîé ìàòåìàòèêè è ìåíåäæìåíòà ÕÒÓÐÝ, èíæåíåð ëàáîðàòî- ðèè ìàòåìàòè÷åñêîãî è êîìïüþòåðíîãî ìîäåëèðîâàíèÿ. Íàó÷íûå èíòåðåñû: àíàëèòè÷åñêîå è ÷èñëåííîå ðåøåíèå óðàâíåíèé ìàòå- ìàòè÷åñêîé ôèçèêè. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. 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ÀÂÐÀÌÅÍÊÎ, ÀËÜ ÑÀËÀÉÌÅÕ ÑÀÔÂÀÍ, Ñ.Â. ØÒÀÍÃÅÉ ÎÏÒÈÌÀËÜÍÎÅ ÐÀÑÏÐÅÄÅËÅÍÈÅ ÐÅÑÓÐÑΠ ÓÑËÎÂÈßÕ ÏËÎÕÎÉ ÑÎÂÌÅÑÒÈÌÎÑÒÈ ÔÓÍÊÖÈÎÍÀËÜÍÛÕ ÎÃÐÀÍÈ×ÅÍÈÉ Ðàçðàáîòàíà ìåòîäîëîãèÿ îïòèìàëüíîãî ðàñïðåäåëåíèÿ ðàç- ëè÷íîãî ðîäà ðåñóðñîâ, âêëþ÷àþùàÿ ìàòåìàòè÷åñêîå îïèñàíèå çàäà÷è â êëàññå ìîäåëåé ëèíåéíîãî ïðîãðàììèðîâàíèÿ, ìîäèôè- öèðîâàííûé ñèìïëåêñ-ìåòîä ïîèñêà ðåøåíèé è àëãîðèòì ïî- ñòîïòèìàëüíîãî àíàëèçà. Ïðèâîäèòñÿ êîíêðåòíûé ïðèìåð,èëëþ- ñòðèðóþùèé ðåàëèçàöèþ ðàçðàáîòàííîé ìåòîäîëîãèè. Ïðîáëåìà ðàñïðåäåëåíèÿ ðåñóðñîâ Åñëè ïîä ðåñóðñàìè ïîíèìàòü âñå òî, ÷òî èñïîëüçóåòñÿ â ïðîöåññå ïðîèçâîäñòâà è êîììåð÷åñêîé äåÿòåëüíîñòè (ëþäè, ôèíàíñû, âðåìÿ, òîâàðû, ýíåðãåòèêà), òî ìîæíî óòâåðæäàòü, ÷òî âàæíåéøåé çàäà÷åé ïëàíèðîâàíèÿ è óïðàâëåíèÿ ÿâëÿåòñÿ ðàñïðåäåëåíèå ðåñóðñîâ. Êëàññè- ÷åñêàÿ çàäà÷à îá èõ ðàñïðåäåëåíèè ñâîäèòñÿ ê òîìó, ÷òîáû èìåþùèåñÿ â íàëè÷èè ðåñóðñû ðàñïðåäåëèòü ïî ðàáîòàì, êîòîðûå íåîáõîäèìî âûïîëíèòü. Åñëè áû ðåñóðñîâ áûëî äîñòàòî÷íî äëÿ ýôôåêòèâíîãî (êà÷åñòâåííîãî, ñâîåâðåìåííîãî, äåøåâîãî) âûïîëíåíèÿ âñåõ ðàáîò, òî ïîäîáíàÿ çàäà÷à íå âîçíèêëà áû.  ðåàëüíîé ñèòóàöèè âñåãäà ñóùåñòâó- þò äåôèöèòû òåõ èëè èíûõ ðåñóðñîâ. Èõ ïåðåìåùåíèå îò ìåõàíèçìà âûïîëíåíèÿ îäíîé ðàáîòû ê äðóãîé ïðèâîäèò ê èçìåíåíèþ îáùåé ýôôåêòèâíîñòè âûïîëíåíèÿ âñåõ âìåñòå âçÿòûõ ðàáîò. Îòñþäà âûòåêà- åò, ÷òî èìåþùèåñÿ ðåñóðñû æåëàòåëüíî ðàñïðåäåëèòü òàêèì îáðàçîì, ÷òîáû îáåñïå÷èòü ìàêñèìàëüíûé îáùèé äîõîä (ïðèáûëü) ïðåäïðèÿòèÿ èëè ìèíèìàëüíûå îáùèå èçäåðæêè (çàòðàòû). Ýôôåêòèâíîå ïëàíèðîâàíèå ïðåäïðèÿòèé èñõîäèò èç ïðåäïîñûëêè î çàêîíîìåðíîé îãðàíè÷åííîñòè èìåþùèõñÿ â ðàñïîðÿæåíèè ðåñóðñîâ, áåç ÷åãî ïîòåðÿëî áû ñìûñë ñðàâíåíèå ðàçëè÷íûõ âàðèàíòîâ ïëàíîâûõ ðåøåíèé. Ïðè îïòèìàëüíîì ïëàíèðîâàíèè âñÿêèé äåôèöèòíûé ðåñóðñ â îòëè÷èå îò íåäåôèöèòíîãî èñïîëüçóåòñÿ ïîëíîñòüþ; åñëè æå åãî êîëè÷åñòâî èçìåíÿåòñÿ, òî ìåíÿåòñÿ è îïòèìàëüíîå çíà÷åíèå öåëåâîé ôóíêöèè. Ïðè èçìåíåíèè äåôèöèòíîãî ðåñóðñà ìåíÿåòñÿ è îïòèìàëü- íîå çíà÷åíèå öåëåâîé ôóíêöèè. Èçìåíåíèå ðåñóðñà ìîæåò èìåòü äåòåð- ìèíèðîâàííûé õàðàêòåð (îäíîçíà÷íî çàâèñåòü îò âðåìåíè), èìåòü ñòî- õàñòè÷åñêèé õàðàêòåð (íàñòóïëåíèå ýïèäåìèè â òîì èëè èíîì ñåçîíå ìîæíî ïðåäñêàçàòü ñ çàäàííîé âåðîÿòíîñòüþ) èëè íîñèòü íåîïðåäåëåí- íûé õàðàêòåð, çàâèñÿùèé îò ðàçëè÷íûõ ôàêòîðîâ. WxmhWϓ&I&vڊZbDaja~VS(P Bѩc" R׊9/|_Dk1ɓ4`Ǟ~={s&bLR4&rvpD43)awmUi̠C v_ gc^9|f<-{ݶ8XR_l72*) L<)`XDՎ]}|qK-N+.y ޔF1.emdzmeQd|V6-P&f r(ч' J +$Mv-{Led:t/Y^t?AN$R Mo5`

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(TuB:Ѳ r:}7BgYJ_SꜲEoN[٨z7fRa^'Ƿ(w/2=qBmmp: h>AӶ<9CybFĜc,_\2uC6Sϲ) OO*|%e?\|PeJf7w_D˯Wx_>%>+t$cf`| zC9uMy-~׃8u>4 tL5crh߸Xurϋ:U%•oqB6)|wHXJp[3*qP}+:k144&Mp O(c.M]to-lC1|c5?ev+gbvҥM0]$aAeNqOq9m]Ã<}i6.ROo'fhBoQL0?!?_KA,E^QI5(xO#rcOfqϫCy@ýqrGON.޵ݵ5 Q ㄅ}U"#]},3;w)51{x-9 fx]2+~)s]'s9XΞ;KJќ=ߘEEc+#=o򷷐|:Z])c fL!}iiI9S |<ف}>*t{ ^YuY.;@](ܧ13G2Ʈ0;*[+R.ժN)Cr/SNo ƕ oS}@ׁv5}m!'JgzN:n?B7i?Z>MgüeGdO24i.: 35|> ߋϐ}}Ϻs4V}Vn ϽBkW >˿Mr|kri We9W{9>I-j9ySEoC8ǷB|)Jg~|[{v{FO}l<}o'Jw٠oKi;{Uo$?_,{(;#9*mz_K,|#[(kԷm)6h\oԆ1OHR;IݬJ9>-M瓉oOvɻYw!H=w'gJΑ;Oٱٿ?21pޑ|3Jo$UoArË=p?LJhwH<F_F^8W޿l雵[{ |m+4}U;Iyq9_WϸqN`ɓY̽imp,J8|\tt̹42; %z;4jEً7%7{W ,%,,52 Çàäà÷è ðàñïðåäåëåíèÿ ðåñóðñîâ Ïðîáëåìà ðàñïðåäåëåíèÿ ðåñóðñîâ âîçíèêàåò âñÿêèé ðàç ïðè ïëàíè- ðîâàíèè âûïîëíÿåìûõ îïåðàöèé, êîãäà èìåþùèõñÿ â íàëè÷èè ðåñóðñîâ äëÿ âûïîëíåíèÿ âñåõ ðàáîò íàèëó÷øèì îáðàçîì íå õâàòàåò. Ïî ôóíê- öèîíàëüíîìó íàçíà÷åíèþ çàäà÷è ðàñïðåäåëåíèÿ ðåñóðñîâ ìîæíî ðàçäå- ëèòü íà òðè ãðóïïû: 1) ðàñïðåäåëèòü çàäàííûå ðåñóðñû ìåæäó çàïëàíè- ðîâàííûìè ê âûïîëíåíèþ ðàáîòàìè òàêèì îáðàçîì, ÷òîáû ìàêñèìè- çèðîâàòü ïðèáûëü èëè ìèíèìèçèðîâàòü îæèäàåìûå çàòðàòû; 2) îïðåäå- ëèòü, êàêèå ðåñóðñû íåîáõîäèìû äëÿ âûïîëíåíèÿ çàäàííûõ ðàáîò, ÷òîáû ìèíèìèçèðîâàòü ñóììàðíûå èçäåðæêè ïðîèçâîäñòâà; 3) îïðåäå- ëèòü ñîñòàâ ðàáîò, êîòîðûé ìîæíî âûïîëíèòü çàäàííûìè ðåñóðñàìè. Ïðè îïòèìàëüíîì ðàñïðåäåëåíèè ðåñóðñîâ èñïîëüçóþòñÿ ðàçëè÷íûå ìîäèôèêàöèè êëàññè÷åñêèõ çàäà÷ ëèíåéíîãî, íåëèíåéíîãî è öåëî÷èñ- ëåííîãî ìàòåìàòè÷åñêîãî ïðîãðàììèðîâàíèÿ â óñëîâèÿõ ïëîõî è õîðî- øî ñîâìåñòèìûõ ñèñòåì ôóíêöèîíàëüíûõ îãðàíè÷åíèé ïðè äåòåðìèíè- ðîâàííîé, íå÷åòêîé è ñòîõàñòè÷åñêîé ïîñòàíîâêàõ. Çàäà÷à îïòèìàëüíî- ãî ðàñïðåäåëåíèÿ ðåñóðñîâ ñâîäèòñÿ ê òîìó, ÷òîáû íàèáîëåå ðàöèîíàëü- íûì îáðàçîì ðàñïðåäåëèòü çàäàííûå äåôèöèòíûå ðåñóðñû, îáåñïå÷èâ âûïóñê ìàêñèìàëüíî âîçìîæíîãî êîëè÷åñòâà òîâàðîâ, îïòèìèçèðóÿ ïðè ýòîì âûáðàííûé êðèòåðèé ýôôåêòèâíîñòè (îáúåì âûïóñêàåìîé ïðîäóêöèè, ïðèáûëü, ñåáåñòîèìîñòü, êàïèòàëüíûå çàòðàòû, óðîâåíü ðåíòàáåëüíîñòè è äð.). Åñëè â êà÷åñòâå êðèòåðèÿ îïòèìàëüíîñòè âûáðàòü ñóììàðíóþ ïðè- áûëü ïðåäïðèÿòèÿ ) x ( F , òî öåëåâóþ ôóíêöèþ â ëèíåéíîì ïðèáëèæå- íèè ìîæíî ïðåäñòàâèòü âûðàæåíèåì âèäà [1-3]: max x с ) x ( F j n 1 j j     . (1) Îãðàíè÷åíèÿ íà ïåðåìåííûå ìîäåëè íàêëàäûâàþòñÿ âûäåëåííûìè ðåñóðñàìè ïî ôîíäó âðåìåíè ðàáîòû îáîðóäîâàíèÿ èëè èìåþùèìèñÿ â íàëè÷èè ôèíàíñîâûìè âîçìîæíîñòÿìè â âèäå ñîîòíîøåíèé: ) m , 1 i ( b x a i n 1 j j ij     . (2) Íåîòðèöàòåëüíîñòü ïåðåìåííûõ çàïèñûâàåòñÿ â âèäå îãðàíè÷åíèé: ) n , 1 j ( 0, x j   . (3) Ìàòåìàòè÷åñêàÿ ìîäåëü (1)-(3) îòíîñèòñÿ ê ïðîñòåéøåìó òèïó ìîäå- ëåé ðàñïðåäåëåíèÿ ðåñóðñîâ â êëàññå çàäà÷ ëèíåéíîãî ïðîãðàììèðîâà- íèÿ.  îáùåì ñëó÷àå â ìîäåëü (1)-(3) ìîãóò âõîäèòü îãðàíè÷åíèÿ ïî ðåñóðñàì îáîðóäîâàíèÿ i b â âèäå ôîíäà âðåìåíè ðàáîòû i-é ãðóïïû îáîðóäîâàíèÿ ) m , 1 i ( b x a i n 1 j j ij     ; îãðàíè÷åíèÿ íà ïåðåìåííûå ïî G xhUu}{mo 6lZM֘ ? 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;G3kP|/J?3 ǧkD KVcV2S5?6uH=k'! }vlE.3:|BK_S(neA<<~9;Cpk'uY{h>.`o'>~G uUUdU [yxV~w ~?~7[tu]oa}o}zMOR1f[, HI@>80&>]<_ߵF60=R/JXzƯJ 3rljB m__n}Kk?5}=F~;=6~x4Ry\!5*:_Er7T׿Wx|*-Ďݷ x Wd:sLLSwEv^/)RҡYyY+e? }|#H[m>9~d߈)+uo9o.䯟za%Vn_י>x• ݱs3^5A*Bf f )8r-j zSj=>P-E]]}?m?UȠ~V~k~+r723&[[{h #S_y.;8\sd2q‡fs`nTk~;zG8!88 sM/&c7Ijg@+5gʑc&:]Bcz 5 Cƴ敛h_?^^1MgmM6{H .Ϙ3N ,,53 àññîðòèìåíòó âûïóñêàåìîé ïðîäóêöèè x j â âèäå äèàïàçîíà çíà÷åíèé êàæäîé èç ïåðåìåííûõ ; ) n , 1 j ( d x d j j 1      îãðàíè÷åíèÿ ïî ðàñõî- äó ìàòåðèàëîâ, çàòðàòàì òðóäà è ôîíäó çàðàáîòíîé ïëàòû. Ðåàëüíûå çàäà÷è ðàñïðåäåëåíèÿ ðåñóðñîâ ñâîäÿòñÿ ê òîìó, ÷òîáû íàéòè òàêîå çíà÷åíèå âåêòîðà ïåðåìåííûõ x R x n *    , êîòîðîå äîñ- òàâëÿåò ýêñòðåìóì (äëÿ îïðåäåëåííîñòè ìàêñèìóì) îäíîìó èëè íå- ñêîëüêèì ÷àñòíûì êðèòåðèÿì y x i k i i    ( ), , 1 , óäåðæèâàÿ îñòàëüíûå y i k m i , ,   1 íà íåêîòîðîì óðîâíå B i k m i , ,   1 : Q x x x k x R n ( ) { ( ), , ( )} max      1  , (4) R x x B i k m i i i ( ) ( ) , ,      1 , (5) a x x b x x j n j j j j ( ) ( ), , ,       0 1 . (6) Ðåøåíèå çàäà÷è (4)-(6) ïðîèçâîäèòñÿ ñ ó÷åòîì ñîâîêóïíîñòè îãðàíè- ÷åíèé. Ôóíêöèîíàëüíûå îãðàíè÷åíèÿ (5) îòðàæàþò àíàëèòè÷åñêèå çà- âèñèìîñòè òèïà áàëàíñîâûõ óðàâíåíèé è ñòàòèñòè÷åñêèå çàâèñèìîñòè òèïà ïðîèçâîäñòâåííûõ ôóíêöèé. ×àñòü ôóíêöèîíàëüíûõ îãðàíè÷å- íèé èãðàåò ðîëü êðèòåðèàëüíûõ îãðàíè÷åíèé   j j x B B ( ) ,     , (7) ïðè âûïîëíåíèè êîòîðûõ ðåàëèçóåòñÿ êâàçèîïòèìàëüíûé âàðèàíò ïëà- íà. Ïàðàìåòðû ôóíêöèîíàëüíûõ îãðàíè÷åíèé îïðåäåëÿþòñÿ ïî ðåçóëü- òàòàì íàáëþäåíèé, ïîýòîìó îíè ñîäåðæàò ðàçëè÷íîãî ðîäà íåîïðåäå- ëåííîñòè. Îñíîâíûìè ïðè÷èíàìè èõ ïîÿâëåíèÿ ÿâëÿþòñÿ æåñòêî ñòà- áèëèçèðîâàííûå ðåæèìû ôóíêöèîíèðîâàíèÿ òåõíîëîãè÷åñêèõ ïðîöåñ- ñîâ, èçìåíÿþùèåñÿ íåñëó÷àéíûì îáðàçîì óñëîâèÿ ðàáîòû è ïðîÿâëå- íèÿ âíåøíåé ñðåäû, íåïðåäñêàçóåìûå âîëåâûå ðåøåíèÿ îðãàíèçàöèîí- íûõ âîïðîñîâ, èçìåíåíèå ïàðàìåòðîâ â ñèëó ñòàðåíèÿ è èçíîñà îáîðó- äîâàíèÿ.  ìîäåëÿõ îïòèìàëüíîãî ðàñïðåäåëåíèÿ ðåñóðñîâ íåîïðåäå- ëåííîñòü ïðîÿâëÿåòñÿ â íåäîñòîâåðíîñòè è íåïîëíîòå èñõîäíûõ äàí- íûõ, ïëîõîé ñîâìåñòèìîñòè ñèñòåìû ôóíêöèîíàëüíûõ îãðàíè÷åíèé, íåàäåêâàòíîñòè èñïîëüçóåìûõ ñîîòíîøåíèé è ïðîòèâîðå÷èâîñòè ñèñòå- ìû îãðàíè÷åíèé.  ìíîãîêðèòåðèàëüíûõ çàäà÷àõ îíà îïðåäåëÿåòñÿ èñõîäíûìè äàííûìè, ðåãóëÿðèçàöèåé ïðè îöåíèâàíèè ïàðàìåòðîâ ôóí- êöèîíàëüíûõ îãðàíè÷åíèé, àïïðîêñèìàöèåé íåêîððåêòíî ïîñòàâëåí- íîé çàäà÷è ñ íàòÿæêîé è ñâåðòêîé ÷àñòíûõ êðèòåðèåâ. 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Âûÿâëåíèå îáëàñòè óñòîé÷èâûõ ðåøåíèé Óíèâåðñàëüíûì ïðèåìîì ðåøåíèÿ ëþáûõ çàäà÷ ëèíåéíîãî ïðîãðàì- ìèðîâàíèÿ ñ÷èòàåòñÿ ñèìïëåêñ-ìåòîä, èäåÿ êîòîðîãî ñîñòîèò â ïîñëåäî- âàòåëüíîì óëó÷øåíèè ïëàíîâ çàäà÷è äî òåõ ïîð, ïîêà íå áóäåò ïîëó÷å- íî îïòèìàëüíîå ðåøåíèå. Ðàçðàáîòàíî äîñòàòî÷íîå êîëè÷åñòâî ìîäèôè- êàöèé ñèìïëåêñ-ìåòîäà ïðèìåíèòåëüíî ê êîíêðåòíûì îñîáåííîñòÿì çàäà÷, ñîâìåñòèìîñòè ñèñòåì ôóíêöèîíàëüíûõ îãðàíè÷åíèé, íåîáõîäè- ìîñòè ïðîâåäåíèÿ àíàëèçà ÷óâñòâèòåëüíîñòè ïðèíèìàåìûõ ðåøåíèé è èíûõ ôàêòîðîâ. Âû÷èñëèòåëüíàÿ ñõåìà âûäåëåíèÿ îáëàñòè ðåøåíèé, óñòîé÷èâûõ ê îòêëîíåíèþ èñõîäíûõ ïàðàìåòðîâ Система плохо обусловлена 1. Блок формирования исходных данных данных 2. Блок исходных данных 3. Формирователь ресурсных ограничений 6. Блок принятия оптимальных решений 7. Лицо, принимающее решение 8. Блок формирования решений 4. Анализатор совместимости функциональных ограничений 5. Преобразователь функциональных ограничений 9. 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Âû÷èñëèòåëüíàÿ ñõåìà ìåòîäà, ïðèâåäåííàÿ íà ðèñóíêå, ñîäåðæèò ïÿòü îñíîâíûõ áëîêîâ: 1, 4, 5, 8, 9. Íàçíà÷åíèå áëîêîâ âû÷èñëèòåëüíîé ñõåìû ïîÿñíÿåòñÿ â ïðî- öåññå ðåøåíèÿ çàäà÷è ðàñïðåäåëåíèÿ ðåñóðñîâ íà êîíêðåòíîì ïðèìåðå. Ïðåäïîëîæèì [4], ÷òî íåêîòîðîå ïðåäïðèÿòèå âûïóñêàåò ïðîäóêöèþ ÷åòûðåõ òèïîâ ÒÏ1 - ÒÏ4 ñ èñïîëüçîâàíèåì òðåõ âèäîâ ðåñóðñîâ, íîðìû ðàñõîäà êîòîðûõ è óðîâåíü ïîëó÷àåìîé îò èõ ðåàëèçàöèè ïðèáûëè ïðèâå- äåíû â òàáë. 1. Òðåáóåòñÿ îïðåäåëèòü âàðèàíò îïòèìàëüíîãî ïëàíà ïðîèç- âîäñòâà ïî êðèòåðèþ ìàêñèìóìà ïðèáûëè è ïðîàíàëèçèðîâàòü ïîëó÷åííîå ðåøåíèå íà ÷óâñòâèòåëüíîñòü ê âîçìîæíûì îòêëîíåíèÿì ðåñóðñîâ. Ïðè ïîñòðîåíèè ìàòåìàòè÷åñêîé ìîäåëè ðàñïðåäåëåíèÿ ðåñóðñîâ îáúåì ïðîèçâîäèìîé ïðîäóêöèè îáîçíà÷èì ÷åðåç õ j , à ïðèáûëü ñ åäèíèöû ïðîäóêöèè ÷åðåç ñ j . Ïðîèçâîäñòâåííûå ðàñõîäû îïðåäåëÿþòñÿ ñëåäóþùèìè ðåñóðñàìè: ôèíàíñîâûìè a 1j , j = 1, 2, …, n, òðóäîâûìè a 2j , j = 1, 2, …, n è ñûðüåâûìè a 3j , j = 1, 2, …, n. Âñåãî â íàëè÷èè èìååòñÿ: ôèíàíñîâûõ ðåñóðñîâ b 1 , òðóäîâûõ ðåñóðñîâ b 2 , ìàòåðèàëüíî-ñûðüåâûõ ðåñóðñîâ b 3 . Ëèíåéíàÿ ìàòåìàòè÷åñêàÿ ìîäåëü ðàñïðåäåëåíèÿ ðåñóðñîâ ôîðìàëüíî çàïèñûâàåòñÿ â ñëåäóþùåì âèäå:                             . 4 , 1 ; 0 ; 100 13 10 6 4 ; 110 3 4 5 6 ; 16 max; 130 120 70 60 4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 j x x x x x x x x x x x x x x x x x F j Ïðè ðåøåíèè ýòîé ñèñòåìû òàáëè÷íûì ñèìïëåêñ-ìåòîäîì ïîëó÷åí îïòèìàëüíûé ïëàí ïðîèçâîäñòâà ïî âèäàì ïðîäóêöèè: õ 1 * = 10, x 2 * = 0, x 3 * = 4, õ 4 * = 0, ïðè ýòîì âåëè÷èíà ïðèáûëè ñîñòàâèëà F = 1320, à ðåçåðâ ðåñóðñîâ ñûðüÿ ñîñòàâèë 26 åäèíèö, ÷òî ñâèäåòåëüñòâóåò îá åãî Òàáëèöà 1 Èñõîäíûå äàííûå çàäà÷è ðàñïðåäåëåíèÿ ðåñóðñîâ Вид продукции Виды используемых ресурсов ТП1 ТП2 ТП3 ТП4 Располагаемый ресурс Финансовые 1 1 1 1 16 Трудовые 6 5 4 3 110 Сырьевые 4 6 10 13 100 Прибыль с единицы продукции плана 60 70 120 130 --- План х 1 х 2 х 3 х 4 --- g&xilTUZ:(RVq jP+[jA F@A@E"|e&$ a &y]3nxNST`^{;9' b$"RDnDցmEˊAd9r,Woě}UOQΊO]Xusb"i_}Ed7lJz-Nq48XhEt>#z6;+8QU9_ة"MD^ Gہ){BIyR+OFÕEW Ӓ'YP(Rxcn5^dɷ2XV 2mѵ߂< LqsD\)5 .vsTW攣kTPNIX bPgXQQQV+ p5tx* RB re0<h~/pv[\+8W{6XAGx0秾N`+빭〉S˜eRÒ64*'|yR_'KlKR_+~r~rÈ ^[?Tl=nBB8ARY&-N .pK@,gz.{dz2g1{Y[S./B)ՋЯE? _x昗qOb5n5s{w?Z߹uu朌S4XҤR9rJXe5}\=@al:t+@b=Rd-dX)ne[Cůa`ute/V}GT ?M}#`=Oe>Ndx#3T`&n K1@_ "b+7x!Z3O"({ZrfݬtKoLͲcYvu䮄C}so NIs}| :xC}p |e_,."mwߟ&ׁ<軽kߎwlw?c)\ o!qviby^B`Tɦ(GM|ۧ@d!pNKȇY3Ar2A7-vcqZ 䁓jb!7aZuuwxmysq­ɐ@9g+jY[r> qshodXO{)kwϖs-1{=[>lzW'3iIpAA GCQt[Fp[8 j8n>sw<':㝋[ięd]y:rb3ff73tK/||+W_~`~ +W &L>LMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:26  E >EE(16v\2\/E1U{Yx̥Guu8&%)4%]!@YbL8)4R7 %o%D5*@VB)UG)USTUn$r8mS5Q_/x]/^R~{^̜933LӿMgM|cok;M7蛦igzLƤwLq0No3szis/_JizT/)? 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U_@jHR'SQv2lk-T|~뇏 ~ ,~(yHphp4mԶ7{~a}ֿX{?ﯗxa~l1nU#'i d_~:9ZF}'g\t5VG;.>vI#Qǟ Moѳ?qg[1cP}udX7۰9e(欭rŋMb6=cKkN޲۷8zoŊ,,56 èçëèøêàõ. Âîçíèêàåò ðÿä åñòåñòâåííûõ âîïðîñîâ: îñòàíåòñÿ ëè ðåøåíèå îïòèìàëüíûì, åñëè óìåíüøèòñÿ óäåëüíûé âêëàä â ïðèáûëü îäíîé èç ïåðåìåííûõ ìîäåëè; ê êàêèì ïîñëåäñòâèÿì ïðèâåäåò ñîêðàùåíèå îáúå- ìà ðåñóðñîâ; ÷òî ïðîèçîéäåò ñ îïòèìóìîì, åñëè ââåñòè â ìîäåëü íîâóþ óïðàâëÿåìóþ ïåðåìåííóþ. Íàçâàííûå çàäà÷è ðåøàþòñÿ ìåòîäàìè àíà- ëèçà óñòîé÷èâîñòè îáëàñòè ïðèíèìàåìûõ ðåøåíèé ïðè îòêëîíåíèè ðàñïðåäåëÿåìûõ ðåñóðñîâ. Ïðè ýòîì èíòåðåñ ïðåäñòàâëÿþò ñèòóàöèè: ÷òî ïðîèçîéäåò íà ïðåäïðèÿòèè, åñëè: à) 6 ÷åëîâåê èç 16 ðàáîòàþùèõ îòâëå÷ü íà âûïîëíåíèå äðóãèõ ðàáîò; á) ïîñòàâêó ðåñóðñîâ ñíèçèòü íà 20%; â) ïðîèçâîäèòåëüíîñòü îáîðóäîâàíèÿ óâåëè÷èòü íà 50%, è êàê ýòî îòðàçèòñÿ íà âûïóñêå ïðîäóêöèè. Èíûìè ñëîâàìè, æåëàòåëüíî çíàòü îáëàñòü îïòèìàëüíûõ ðåøåíèé, óñòîé÷èâûõ ê îòêëîíåíèÿì ðåñóðñíûõ îãðàíè÷åíèé. Êàê èçâåñòíî, êàæäîé èñõîäíîé çàäà÷å ëèíåéíîãî ïðîãðàììèðîâà- íèÿ ñîîòâåòñòâóåò îïðåäåëåííàÿ äâîéñòâåííàÿ çàäà÷à. Åå ïåðåìåííàÿ, íàçûâàåìàÿ äâîéñòâåííîé ïåðåìåííîé, ïîçâîëÿåò îöåíèòü âëèÿíèå èç- ìåíåíèÿ êàæäîãî âèäà ðåñóðñà íà öåëåâóþ ôóíêöèþ (â ñâÿçè ñ ýòèì äâîéñòâåííûå ïåðåìåííûå ÷àñòî íàçûâàþò äâîéñòâåííûìè îöåíêàìè, ïðè ýòîì ñóùåñòâåííî, ÷òî äëÿ íàõîæäåíèÿ äâîéñòâåííûõ îöåíîê íå òðåáóåòñÿ ðåøàòü äâîéñòâåííóþ çàäà÷ó). Çíà÷åíèÿ äâîéñòâåííûõ îöå- íîê óæå ïîëó÷åíû â ñèìïëåêñ-òàáëèöå îïòèìàëüíîãî ðåøåíèÿ èñõîä- íîé çàäà÷è. Óçíàòü çíà÷åíèå äâîéñòâåííûõ îöåíîê ìîæíî ñëåäóþùèì îáðàçîì. Åñëè íåêîòîðûé i-é ðåñóðñ èñïîëüçóåòñÿ íå ïîëíîñòüþ, òî äîïîëíèòåëüíàÿ ïåðåìåííàÿ â îãðàíè÷åíèè äëÿ äàííîãî ðåñóðñà áîëüøå íóëÿ.  àíàëèçèðóåìîì ïðèìåðå òàêèì ðåñóðñîì âûñòóïàåò ñûðüå b 2 = 110 è åãî ðåçåðâ ó 2 = 26 (åñëè áû ñûðüÿ áûëî íå 110, à 112, òî ðåçåðâ ðàâíÿëñÿ áû íå 26, à 28, ïðè ýòîì óâåëè÷åíèÿ öåëåâîé ôóíêöèè íå ïðîèçîøëî áû). Òàêèì îáðàçîì, åñëè ïî îïðåäåëåííîìó ðåñóðñó èìååòñÿ ðåçåðâ, òî äîïîëíèòåëüíàÿ ïåðåìåííàÿ ÿâëÿåòñÿ áàçèñíîé, à åå äâîéñòâåííàÿ îöåí- êà ðàâíÿåòñÿ íóëþ.  ðàññìàòðèâàåìîì ïðèìåðå òðóäîâûå ðåñóðñû è îáîðóäîâàíèå èñïîëüçîâàíû ïîëíîñòüþ, ïîýòîìó èõ äîïîëíèòåëüíûå ïåðåìåííûå ðàâíû íóëþ. Åñëè ðåñóðñ èñïîëüçóåòñÿ ïîëíîñòüþ, òî åãî èçìåíåíèå (óâåëè÷åíèå èëè óìåíüøåíèå) ïîâëèÿåò íà îáúåì âûïóñêàå- ìîé ïðîäóêöèè è â êîíå÷íîì ñ÷åòå íà öåëåâóþ ôóíêöèþ: îíà óâåëè÷èò- ñÿ èëè óìåíüøèòñÿ íà ðàçìåð ñîáñòâåííîé îöåíêè. Çíà÷åíèÿ äîïîëíè- òåëüíûõ ïåðåìåííûõ è äâîéñòâåííûõ îöåíîê ïîêàçûâàþò, ÷òî ïðè ðîñòå òðóäîâûõ ðåñóðñîâ íà åäèíèöó öåëåâàÿ ôóíêöèÿ âîçðàñòàåò íà 20 åäè- íèö, äîñòèãíóâ çíà÷åíèÿ F = 1340, à ïðè èõ óìåíüøåíèè íà åäèíèöó ïîëó÷èì F = 1300. Ðîñò îáîðóäîâàíèÿ íà åäèíèöó âûçîâåò óâåëè÷åíèå öåëåâîé ôóíêöèè íà 10 åäèíèö, ò. å. ïîëó÷èì F = 1330, à ïðè åãî ñíèæåíèè íà åäèíèöó F = 1310. !xLUeǟs ׋^.~\RJM̹XN˘03cll bL!D?1ښ*M=}{;wpn;gyϹg'b[f,K|"ALl\V"o$q۷4qm͵ C4XjA_kf,g!/Ҭ4GMxt0JK!˶ _ =meP9:reZ͸!Teo2x;7-_J~ x-9d'(oGǙ{.cbaaב{{- ak-bҌcnQXc= n~K_Tq/gɿ}g3z%.jwk0H_/{~QF+@[t=>*9{%]|T0_~#ֺ^2]K{S‹p~Zr֮Lg|}9El{>P&dO+sZ@75YhOb ۅs=s]"p%x > x }h|\g?@3G7h%bE`6󽏯guEll<;^,И>gA{ R]\VDŸbP 638~hM}=1rXBs_!Ƅd̡yԈpgtU̞J'k~&b(Mnv6SꞦל~C8u][έړՙ,q˹kO5fp~7!97;u;}*hTyN,~#SaꥢY}$|'獟}3Z'Θu^x:u`L z:uӸMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:26  y] yy(16̑2/y1@{(x͝ ]Uu I4LHr1ʨ(3Pb1` [P>ŖOiEE5-b*hDLsΞw Tgk{}=ʲ"wggT>og˲l,Oy +,+}ʪ_e7e?D?G-'[pɸlIv^,W9+{UA,[.['T!&F]/52zEUvkT+=])*H?_/Iw_#4U0g,VUɹFlфPu g=U:c[s԰1\s)lg r}p'|v8aJg lJvڑ_x~CQkxVWmT>+CxKOyL]=I{{=+ 0K:r,Ʞ?rsQ kD4A8_+bk K*9@ jYv`~6 ߀)a:5=xDyp,[r =]8MU|fKv./6e}uo?~Qz+\j\R[<@ &/%?\˭dz~*КYUG9L2>c='>Ms||ǎ߭ \J>vdy@׹J'66Ć=@ u+T5=/Dυm{'H\+V-y`',;]КPo|N2А*g^ѭ{zSObZ< `hMK^̛-5}@kⓓh󅒁+jCk"@r8|Y"ZgWՒ(Z~`TΧE2痂>>W> @kYCu]\ڋg8%֏ދ=J>F|e/UTG͡!*^Ыᨖv{G~sJ'&z#g* 5a=%/T:Bk+ ZZcJ'{U~XOhM\X+8IEZ$=?& mob%\>.%55n%`ݚCCO:sy_Q?c`hM@@C{0Cx`hM|ϟW wIg͎YL5#NVXhEK}>@C1,-<dtNFψ1JXku+*p_h}`vpJ8Wx`jzORwdV_h*\J$UbW}Ȯ *z~@XOhMBZ+z$X9`|`C5{풉>Â>>J^e߭@^|O 7KԜvh|˰尞{B㻦|o=c}7ה'<,Eg[r6MwOY*Ogӧ{w*8gDﷂxY c)/< u: WD|G+swt. ; eZ  d]02 ejs`G꿛8;<|yo36<|ӝ=_ܳ&J[\~>&0 y֭{H|O?lY] &)spnϞ송\0\ 7Փ_kMxiI?RnɯuO?֔óS6bE/z`͍~SOlivr^8;%{8귉r+O' .?~v?rgLerb/SpNL=w:/|(g|4K]2qm:˯I}뇒cݩ_˯<\l돚' ^:~B_܉ƥ<|&ծ/rW*Ơ6yHOal󑇤lӉ_!RL5 Cn돚OXwUr ~UA.Q90 2NyU>|.mp[~ǧx.6 \x6?}K>n3dP7hӄ;^)n?Hl~t?TM:߮_Ifמs-߭*}w?ݏ;Aro$ʙuoW~RfbmL[3%%iˡ)Bo|g[c*؋9m//~׶,O x0tYf(9c2/-sMn7Q4F/=8Q6Vo|[e7dyR-Ce;tF%񽈝zgЙ2]W:( x[3Ï]\*|gid*/Fu#z^~kU'uwTg !U=f,uIhCq[TPS|_i|w{cƘğ|m[]6F>&$|ދsX}ma~dzT,㟭C\qܯ"W˷sveҐޅIȻ8;%ϋ,{bÞ'0y.WqܸMwȦo3M0Oq;Ck'𕒁WȇD~8|dZ8/O'#2~gqBk2Y~EmM@2_zP֝3{pؾJ456ߑ[kCx-c-Y1?(ώOǒ cX"%8?Ѕv\{*2Wq.Aw; ݚΐN'!4l]S6k|dȇD~dP<OhK'$_+Zϑ|~+eL{^'SGc^om@.gѝE2#fjI9roY iksrF;SH9kאxnYSxh/\<;@ eסü8H>+>r^o #%X\#ZEV?]j΋ wY,Gp"0~81~m/!;g;2,{IƋcߩCphgf{oͳ3 Xt8uNآ8n}M\7&9׎ɪSkxaȱ,cY-5/.}+v>Tiݍo}hgK_D,ܝ{s{j+NWsA m?7ݱQ^amHZ38>؊oG&@J_~92ڟnԘ7 }$'O7I]|hM/WS(bwbHDWc?߃5~3DXcdtӱ1Yj5qR_I8] N#P:P.9a*8@ vc탏&/⊘'vh,+M=-|Ɲ`Ix‹_U6y+upl=lmZKٜ댨|'Ti\6ŮԽö}B{*ЈC49;B);\-Zxz=~PX}$ޔ</- XCci~8ˇ_fj,[,Ŀ66zU%;n咇,_Zْ {`ꘀvjrV(܈cglUOB10Vwg jʉ*+8N-=g|}CĀoWȡh<<_PN=S>I\;/gGQI#s<.0;UCNk"3D.6V7!<{{gk2e҆|<~zUysWH~.44Q|)?-m%@R2&mBmϔt`4t wR:`5>W ]#}RrˏUB;+TEQwm xrQ Q1{:8vD>QxU~o2>[4ڤ|Zw Y'mO/ż\sYr_ۤFNq>ІECǔ>|x Y^tl/hkH)xa~%uƎ|pjG]u_l x?C>XC\wLR9L>*#RrN?h .)OΐЃ~u c3Vk4=BnxkRc%ڽGbKkCk"@W%Gcߍ_ ONZ>kɕOH'Wb@cr c$򇲑c7\HSͱAz:8Ɖcp!_on뵢qoKqRAm8)kHvc#X>z]ztm(On{1Z}Ƽ oxyJ;Z74G{C#K9׉FzWY86GGϋ9u Z)᥎2GlkR3jwl}z॑͡]RR6g_R7ޫOɗاdf=%czFmsh/ {Xkl@84b|m/Y$XӰ)se)4lJl:>m55\k W%߬ꘀOzd0~#9hZh,}_֡٧s&>rv yola@pO_j6:g vqzƗ zyu9u¿Oz_:~ZHhgz}ljClchؘg)/m$F9t@8UcȼN35t^+ H:O R=Z߱t=H|XWhtM)Xn!~R0 $u%Ki5ԓ:9w%9gKx,C \?Q=mfK^A=⻈ NxvYJ|fF H!&<} ?˵z[W+Ưg wڴ`\NiyMB=ͺnaVdfن{Mr_K!C~nyCq ߗs5:ۿx)Y_7 |O}kۗkPʡN/W1, 8Ӂ*nϘ Y֫_ҧ*^U˅{xS>M4;1F"],x^7]dvm]$ 臄#';^z3;m޶q9/9\*_K?-h>t !+WdЎ+~ cop'E"C?*Ϗ-|8/U~oxzR3()-W-;uRe{a_tbK56Fr <\k,q¹O-Lp5x\qmv9|S5>||hcU=c!gC'흽1ό^<;f5ƫx< m3lv985u}\:1Fd<km 4z,ly}^Ȃ_UׇZaVODR t^]xvyw;&3=.wD+-5m n 8=Ã,{:α5>?׎q7 9:zP̽Kwq9˗m~i\+T Mb@pl?g n_Z&dWi57Qq~dpOL޽L;k|6ƺ'}R0V K9to[lnaB'Y,,57 Àíàëèç ÷óâñòâèòåëüíîñòè ïðèíèìàåìûõ ðåøåíèé Ïðè óïðàâëåíèè ïðîèçâîäñòâîì âàæíî óìåòü ïðèíèìàòü ðåøåíèÿ â óñëîâèÿõ îòêëîíåíèÿ ðåñóðñîâ îò ïåðâîíà÷àëüíî çàïëàíèðîâàííûõ. Ïóñòü ìàòåìàòè÷åñêàÿ ìîäåëü çàäà÷è ðàñïðåäåëåíèÿ ðåñóðñîâ çàäàíà êðèòåðèåì îïòèìàëüíîñòè F(x 1 , õ 2 , õ 3 , õ 4 ) = 60.00õ 1 + 70õ 2 + 120õ 3 + 130õ 4 , (11) ñèñòåìîé ôóíêöèîíàëüíûõ îãðàíè÷åíèé 1,00x 1 + 1,00x 2 + 1,00õ 3 + 1,00õ 4  16 +   1 =  1 , 6,00x 1 + 5,00x 2 + 4,00õ 3 + 3,00õ 4  110 +   2 =  2 , (12) 4,00x 1 + 6,00x 2 + 10,00õ 3 + 13,00õ 4  100 +   3 =  3 è îãðàíè÷åíèÿìè íåîòðèöàòåëüíîñòè ïåðåìåííûõ . 0 х , 0 х , 0 х , 0 х 4 3 2 1     (13) Áëîê ôîðìèðîâàíèÿ èñõîäíûõ äàííûõ çàäà÷è ðàñïðåäåëåíèÿ ðåñóð- ñîâ (11)-(13) çàäàåò íà÷àëüíîå è êîíå÷íîå çíà÷åíèå èçìåíÿåìîãî ïàðà- ìåòðà, à òàêæå øàã èçìåíåíèÿ ïàðàìåòðà êàæäîãî ôóíêöèîíàëüíîãî îãðàíè÷åíèÿ. Ðàçíîñòè ìåæäó íà÷àëüíûìè è êîíå÷íûìè çíà÷åíèÿìè èçìåíÿåìûõ ïàðàìåòðîâ îïðåäåëÿþò ñóììàðíûå îòêëîíåíèÿ ñîîòâåò- ñòâóþùèõ ðåñóðñíûõ îãðàíè÷åíèé, êîòîðûå îáîçíà÷åíû äëÿ òðóäîâûõ ðåñóðñîâ ÷åðåç   1 , äëÿ ïîñòàâëÿåìûõ ñûðüåâûõ ðåñóðñîâ – ÷åðåç   2 , äëÿ èñïîëüçóåìîãî îáîðóäîâàíèÿ – ÷åðåç   3 .  ðåçóëüòàòå äåëåíèÿ îòêëîíåíèÿ ðåñóðñíîãî îãðàíè÷åíèÿ   j íà íåêîòîðîå ÷èñëî [4], ðàâíîå ïîðÿäêà 3  5, ïîëó÷èì âåëè÷èíó øàãà èçìåíåíèÿ ïàðàìåòðà  b j . Íàïðèìåð, äëÿ èçìåíÿåìîãî ïàðàìåòðà òðóäî- âûõ ðåñóðñîâ ìîæíî âûáðàòü íà÷àëüíîå çíà÷åíèå  1 = 16, êîíå÷íîå çíà÷åíèå – 10.00, øàã èçìåíåíèÿ ïàðàìåòðà  b 1 = 2.00. Òîãäà ðàñ÷åò- íûå çíà÷åíèÿ òðóäîâûõ ðåñóðñîâ áóäóò:  11 = 16,  12 = 14,  13 = 12,  14 =10. Äëÿ èçìåíÿåìîãî ïàðàìåòðà ñûðüåâûõ ðåñóðñîâ ìîæíî âûáðàòü íà÷àëüíîå çíà÷åíèå  2 = 110, êîíå÷íîå çíà÷åíèå – 70,00, øàã èçìåíå- íèÿ ïàðàìåòðà  b 2 = 20,00, ðàñ÷åòíûå çíà÷åíèÿ òðóäîâûõ ðåñóðñîâ  21 =110,  22 = 90,  23 = 70. Ïðè èçìåíåíèè êîëè÷åñòâà èñïîëüçóåìîãî îáîðóäîâàíèÿ ìîæíî âûáðàòü íà÷àëüíîå çíà÷åíèå  3 = 100, êîíå÷íîå çíà÷åíèå – 80,00, øàã èçìåíåíèÿ ïàðàìåòðà  b 3 = 10,00, ðàñ÷åòíûå çíà÷åíèÿ òðóäîâûõ ðåñóðñîâ  31 = 100,  32 = 90,  33 = 80. Âû÷èñëåííûå çíà÷åíèÿ öåëåâîé ôóíêöèè ïðè âàðüèðîâàíèè òðóäî- âûõ è ñûðüåâûõ ðåñóðñîâ, à òàêæå êîëè÷åñòâî èñïîëüçóåìîãî îáîðóäî- âàíèÿ â óêàçàííîì äèàïàçîíå çíà÷åíèé çàíåñåíû â òàáë. 2. Îñíîâíîå íàçíà÷åíèå áëîêà 8 (ðèñóíîê) ñîñòîèò â òîì, ÷òîáû ðåçóëüòàòû âû÷èñ- ëåíèé, ïîñòóïàþùèå ñ áëîêà 9, ðàñïîëîæèòü â ñîîòâåòñòâèè ñî ñòðóêòó- ðîé òàáë. 2. Áëîê 4 ðåøàåò çàäà÷ó î òîì, ÿâëÿåòñÿ ëè ñèñòåìà ôóíêöèî- íàëüíûõ îãðàíè÷åíèé õîðîøî èëè ïëîõî îáóñëîâëåííîé. 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Ïðè óâåëè÷åíèè êîëè÷å- ñòâà èñïîëüçóåìîãî îáîðóäîâàíèÿ ñ öåëüþ ïîâûñèòü ïðèáûëü âûïóñê ïðîäóêöèè x 1 öåëåñîîáðàçíî óìåíüøèòü, à ïðîäóêöèè õ 3 —óâåëè÷èòü. Ýòîò ôàêò îáúÿñíÿåòñÿ òåì, ÷òî ñîãëàñíî èñõîäíûì äàííûì ïðèáûëü ñ åäèíèöû ïðîäóêöèè ñ 1 = 70, ñ 3 = 120, ò. å. åäèíèöà ïðîäóêöèè âèäà Ï3 â 1,7 ðàçà (120/ 70 = 1,7) äàåò áîëüøóþ ïðèáûëü ïî ñðàâíåíèþ ñ åäèíèöåé ïðîäóêöèè âèäà Ï1. Ïîýòîìó öåëåñîîáðàçíî ïðåäóñìîòðåòü ïåðåðàñïðåäåëåíèå âûïóñêà ïðîäóêöèè. Ñïèñîê ëèòåðàòóðû: 1. Àâðàìåíêî Â.Ï. Óïðàâëåíèå ïðîèçâîäñòâîì â óñëîâèÿõ íåîïðåäåëåííîñòè. Ê: ÓÌÊ ÂÎ, 1992. 48 ñ. 2. Àâðàìåíêî Â.Ï., Òèìîôååâ Â.À., Ïàíàñåíêî Â.À., Òàòàíîâ È.È. Ìîäåëèðîâàíèå îðãàíèçàöèîííî-òåõíîëîãè- ÷åñêèõ ñèñòåì. Ðÿçàíü: Ðóññêîå ñëîâî, 1996. 224 ñ. 3. Àëü Ñàëàéìåõ Ñàôâàí, Êàëà÷åâà Â.Â. Ìîäåëèðîâàíèå îïòèìàëüíîãî ðàñïðåäåëåíèÿ ðåñóðñîâ â ëîãè- ñòè÷åñêèõ ñèñòåìàõ.  êí. Âåñòíèê ÕÃÏÓ. Âûï. 93. Õàðüêîâ: Èçä-âî ÕÃÏÓ, 2000. Ñ. 199-204; 4 Øåëîáàåâ Ñ.È. Ìàòåìàòè÷åñêèå ìåòîäû è ìîäåëè â ýêîíî- ìèêå, ôèíàíñàõ è áèçíåñå. Ì.: ÞÍÈÒÈ, 2000. 367 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 26.05.2000 Àâðàìåíêî Âàëåðèé Ïàâëîâè÷, ä-ð òåõí. íàóê, ïðîôåññîð êàôåäðû ÈÓÑ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: èññëåäîâàíèå îïåðàöèé. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-94-51. Àëü Ñàëàéìåõ Ñàôâàí, àñïèðàíò êàôåäðû ÈÓÑ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: êîìïüþòåðèçèðîâàííûå ñèñòåìû óïðàâëåíèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-94-51. Øòàíãåé Ñâåòëàíà Âèêòîðîâíà, ñîèñêàòåëü êàôåäðû ÈÓÑ ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: êîìïüþòåðíûå ñèñòåìû è ñåòè. Àäðåñ: Óêðàè- íà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-94-51, 41-23-11. 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ÕÀÕÀÍÎÂÀ, Â.À. ÏÓÄÎÂ, À.Ë.×ÀÌßÍ ÌÅÒÎÄ ÀÍÀËÈÇÀ ÄÎÏÎËÍÅÍÈÉ ÒÅÑÒÀ ÖÈÔÐÎÂÛÕ ÓÑÒÐÎÉÑÒ ÄËß ÎÖÅÍÊÈ ÅÃÎ ÊÀ×ÅÑÒÂÀ Ïðåäëàãàåòñÿ ìåòîä àíàëèçà äîïîëíåíèé ê ñîñòîÿíèÿì êî- îðäèíàò òåñò-âåêòîðîâ, âåðèôèöèðóþùèõ öèôðîâûå óñòðîéñòâà, â öåëÿõ äèàãíîñòèðîâàíèÿ èõ íåèñïðàâíîñòåé. Ìîäåëü óñòðîéñòâà ïðåäñòàâëåíà ñòðóêòóðîé âçàèìîñâÿçàííûõ ïðèìèòèâíûõ ýëåìåí- òîâ âåíòèëüíîãî è ôóíêöèîíàëüíîãî óðîâíÿ, îïèñàííûõ êóáè- ÷åñêèìè ïîêðûòèÿìè â òðîè÷íîì àëôàâèòå. 1. Ââåäåíèå Äëÿ ïîèñêà äåôåêòîâ â óñòðîéñòâàõ, ðåàëèçîâàííûõ íà îñíîâå ïðî- ãðàììèðóåìûõ ëîãè÷åñêèõ èíòåãðàëüíûõ ñõåì – Field Programable Gate Array (FPGA), Complex Programable Logic Device (CPLD), íåîáõîäèìî èìåòü ñðåäñòâà ìîäåëèðîâàíèÿ èñêàæåíèé ñèãíàëîâ, â êà÷åñòâå êîòî- ðûõ ìîãóò âûñòóïàòü äîïîëíåíèÿ ê èñïðàâíûì ñîñòîÿíèÿì ëèíèé öèôðîâîãî óñòðîéñòâà ïðè ïîäà÷å íà íåãî òåñòà. Ïðåäëàãàåìûé êóáè÷åñêèé ìåòîä ìîäåëèðîâàíèÿ äîïîëíåíèé îáëà- äàåò ñâîéñòâàìè: – çà îäíó èòåðàöèþ âûïîëíÿåòñÿ àíàëèç âëèÿíèÿ äîïîëíåíèé âñåõ ëèíèé íà èñïðàâíîå ñîñòîÿíèå ïðîåêòà ïðè ïîäà÷å î÷åðåäíîãî âõîäíîãî íàáîðà, òàê æå êàê â äåäóêòèâíîì è ñîâìåñòíîì ìåòîäàõ [1-5]; – ìåòîä èíâàðèàíòåí ïî îòíîøåíèþ ê âåíòèëüíîìó, ôóíêöèîíàëü- íîìó è àëãîðèòìè÷åñêîìó óðîâíÿì îïèñàíèÿ óñòðîéñòâà; – ìîäåëèðîâàíèå îñóùåñòâëÿåòñÿ â òðîè÷íîì àëôàâèòå, ÷òî ïîâûøà- åò àäåêâàòíîñòü ðåçóëüòàòîâ àíàëèçà â öåëÿõ äèàãíîñòèðîâàíèÿ öèôðî- âîãî óñòðîéñòâà; – òåõíîëîãè÷íîñòü ìåòîäà äåëàåò âîçìîæíûì åãî àïïàðàòóðíóþ ðåàëèçàöèþ â âèäå IP-core. 2. Ìàòåìàòè÷åñêèé àïïàðàò àíàëèçà ïðèìèòèâà Àâòîìàòíàÿ ìîäåëü ôóíêöèîíàëüíîãî ïðèìèòèâà ïðåäñòàâëÿåòñÿ â âèäå: M=, ãäå X=(X 1 ,X 2 ,...,X i ,...,X m ), Y=(Y 1 ,Y 2 ,...,Y i ,...,X h ), Z=(Z 1 ,Z 2 ,...,Z i ,...,Z k ) – ìíîæåñòâà âõîäíûõ, âíóòðåííèõ è âûõîäíûõ àâòîìàòíûõ ïåðåìåííûõ, îòíîøåíèÿ ìåæäó êîòîðûìè îïèñûâàþòñÿ óðàâíåíèÿìè: Y(t)=f[X(t-1), X(t), Y(t-1), Z(t-1)]; xmheǯ3=/;uXN3X.*DAZFMh6dV旂ZEb,}(шt,#2Yj 9:XR30fk1VMfk d@b׸Jp\fm5!n8zf ‘2g̗ŲHrTr28eJ\X9/fGqv!g#Ų*Od:SWKXwJDvTbrL.LLߩf3Gj9rHKRQ9ᆽ bdMj<ÄVOjSέp j{v3k,b 5vS%:9ò#iwN{18 M`JIJkVGN_v# wgӺh0=fDwA;գx > Sq8kƉ ~4"ޏȀ5~ƶ[5MNu @`?1/ ;'mG9 b"Y{e8O-17@O~ZЫ됏=ʾsβk²-3L.$Wc[ĺ |Pg|&?>lUTp;[ߍ5s~YgAN ܷ X{#WkEn }Svqbz1 1ow6̞73Gk;5MN 6oJ3So?u"L|ӹ~9::Й -~Cr и|>\ :K~ _6rjb4WZU˭M/%ͭ;_n7g T/[竭P]u^\`k=^x:u;;5-Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:26  N4 NN(16_2`/ N1Xr[:{hx _Uu1j_24 P %@y5|4|WhI+}DhZZ ]hcfStE}<2 IH0h`w3g$`ιw}9{s{ӑeqYv}읯QȲWdYSߗeٲ; $`yŷ]ʲ YG#n-...ήrr51V9 &qԐsVMWO )]\V&`pDA?Ul&糀@p^+K(8h`4mK6:@unqKv)HHX%syLγ(Wd9u/a<;ϲל+&N;t΄{Uky/8Ը o,;?-ˮoe x]_sւ蝸+/2\O!}p2ʫ#LZu'mP#-ǟt-(gKͶ顮@^K)Ki_aY9֟ww\{3y]l)bs@U:JpTfl64 [i#tUxťdSN6YW(6ZZ?IBUXQjyYvd͗qso/~܄fN/Am_n+:yCw|86(N<9UnIMuv)>h:ʹt86vv8cj΂Oa_}LG`_~387GO^<}ܚ24zMeS-ːAWQf<]̓&S<eٔiȃpyxnj4o(q@̔i,bLDCȟM)\/6<OB]ȰOOi߱r2,E6%Evmv|8˵7tx`\˝#5uFO.kd>&zoL}$Qpmq-GX/cCűh ŮOSc[N?VDѾ^[XwNdˎ}zkz\/.֑n=^K82[ĵDc D|)rrўx#+_ pMkЎ'\>.F$=_#+ u qu4[}p&1cmǸq3BS;ņcGE uo6H{ӕqn=njx<)Hv n_Џ1cͨ_Gc`t~dmPkZ+5!HX"kʍOP|':{n{fS9p݌{'"?}πFζ Xnޅ1PpM2t"/]>0o|Z~K)ky=ol Kk_ z',Mo5Ipۦwؖ8 >C-!ʣf4O/#O\Zɱ 9?DNP ge-K Ței.^l3'2ßYyUvKgŴ p-Tk[>mק vYKO"Cݾun7W9䉔恶Ӥ7.HkGsV=dI4u!65ޣ-+ CkdQS֎ҞRwnL=@z)moCRu= }7}Co@zCzJS7P4롕1s7)y5yx㕥h9`DOSE.isή5lxQ7cq(仡jZ%Ͷ(Z͙.Ї!| Cη)Lvdkm4dh8u{Ik^+si_ZN=:4mw!+s h;>R[)IS7lӵOR#=}ou}pY#M}F> pގ񴯮(JkO׏z] սu e]Wi{KןҖn*=]?^|QW麮ut|;qnܷʷ%'W~mu^Ӫ5/Ɓkxq3:%8y-}ۼ)95\ߎ^@ Yin6|G\1}g'&ޥy/(VSȰqj֫r{3s@~uTt2SusK}+[~?\8'TNwƔ 8N9r7#,ʯK M{-Ȱ_f7lʘU'|gǻ!i,3 V[:yu-o?ѷO3g6SvXy |pM^ kY Ѿ%x/ҷ[z1և9o'~lJǢc1\sǜ:L@z:޵cVWf)DZ|pUږw[O藥8|#.Ga},y =m5J3vE< c5aecfp F=bT}HyN?Z{^WvEg?O!c#oܷ&_ڄ6/F'쵔sj)o}l7/[ppnlMkYXO^4,K9u  2)GeYvYڮeȲ~==󃰷8>74nB+ߨw#>ě_ ;^Vn~QķS=9ۉ묥6vR, 8zιrb\xW? ey؎W? ͊2Q> dj_Pd-e?bk?uOa JmyEW'm^iN]X 4UvUkXg^g;!?②ݎMvôvSlvr ڠڀ"GN GkQ@SuLF΂6;yrV~ү2_u\KYQZ;:^lP}d_ui|o96nF\ͩ眥vuҵW}/mzտ{#7V=潂:,W |6ʑ+عcr ~AW|`宾WW`y㌲lz`FMW߃+:oV235/\jhG iw}GsEstn)|# y#_D13wp :oǮ/:v;Ÿb ǵe뻞>x.M!.Sukm| W +lla EFvbÑ?ss3,=G͵v'SGA[hOKyb=6ƊW6ur 'u"u-Rvo_Gtťb=/8_\ Lg拴{i'_8҇W巀嗜>~s%\SP難Zvsჸ ym%22^|O}&8yͯhR u7PηN0~:o^u:WKh8'>xP/OږW{^kq˦w=WGV>=f޾|?]K6;ߓA`^K^ֻ|ˁYZ:YƇ|p|*ד}17;3l[9_*Iީ{YG軀&Bٳ+.)ُ?~łKop>w*\_s@ĎV#[?BZqwdDi}A:8o^6pbuEb!GXg=lcـ 3yO*SuI};S<,xGGOp{ɔܗ,ʝPu {qS]鷡 sgy{oGxFD hkmjuog,uz ^y}rv/2:oi_-}>c|50&}9S{Hwfo 7~gt~so<]왴k!O;_'v/l֎u?_C^胼1,My3oq>ZGZ'N_+ y.Wns~"s>8.ί~>X+_Bq:~N޷'iuhG'u-s@6&Ui^5w.NW ۷>Iyc>[ (3Ƈm?/9 ^Xu_g)#tY+)s!VsgoܣxKAzi=ЦZ16g zHOqfN/>hGAyK}P71|!N[GnjFKeȏzg<ρX^%eċ6z8pl _|$cyOYG zA/wpg}^1El?ڶ9.=DZ}Gϕ yiHc_)8s^~vh}=_ڕ_+2#l{锽cd׷(zIS/+g6Hw &]y}g]irxF]O2w HSo,h2MK'|?e]Oiy!W]>SO{ROk)m,il!ʺbqvFzy=|u;s2@zG.5yw zDye4QE&*r'WrB4bFiG5]3ԡiw"S#;ɇ4˽$un/i*K+|Sߥ%Mhў^#A)IS76ksQ֞>#9u}7Ӵ>I 8o5wgu]Du}wEG[꺙t-QW麮uty'6obji뒸7qU.4xmn眚Ģ:(zT5!$p98ה wc>ŽyuWAsx8[uǫw7W<&a>օ #Ps1Q}ZS+= #׾ [,; $= p^9?WR.hBh/8wE1}:'\<3y&_퇱6M㌳Kqpzf}y?m3muq}kv c#fNbWU ])U[E?lϮ{㞿>uݥ%j`,cחbp~t`Z>p}pp^|ϱ|7; #o|;ݎFSί"ͧڈ/_{kIo0>'7% ߇waw2cIޙ GkG$oq"rFNl1Ms:&}йwM׭Ȳ] ]]_wM"Fl_c>-9npO9Qsi (3 }__[E빗`rpU7?9HSoՆWy[&_"ǜ)n&k_+r%3G~,E3mma1Mιi|o k+[o7zL[瘏X* _\"Ryrs^ǚ9 yKSLg9=';æ?2*sZ2uVLخ6I[Lo>`k̞^ˬOO0fޥgc⁛gU@t7C{v? Zsn췧\O_{>n<Ƀ'fѹ]+9_LQ?'59u=ڸ=N0nB=nK3n[gqj~Yq`N+}mߒ3$cs30/G,5>!H?NUpir8nQNS!qyg2ڻ_H*O${95_V~.6cc]$}X}hx 7Vz\T<x|PwAųDZ&_x`_zf򽑦x|/4пWێ'"}5[o@w)q,kC漢~罽t{6x&M>yG'2 r9rϬ ra}yl24e^GR7 \oE(.oNހG&~ MHFUhtuQ- eozoN&2.pm߅ nevb޺˱y5յ({v clߍ/i7yO0YuFyVbMX#ԯw7dL]L1y]yҌyG0b];_}_&\O$|uK;MfynOL;gǷӃډeKiĽ{FG5zqW\`)x 2(ό-}hL\~iږN2Ji ߳ %!̧ j˭>˘SXt ݷ(_-YFIx﹠mH2,iS^g$G}gj_s(3 u@U^Ly^ C(WF~G˧>Ƕ"QN ʑ&_7IYtF" ,^ʯQ*G_{쌷U"oS2~#~~ޥvڮ-X-ï-Z٣for,Z~P[;bAzw;g o94ss7= y0/5=<ƵyWh W\S^r 4Cgd(wuޭ/_y5:wL69NxW3܃0V҅"{._1k|\.ҌW1n<<;n٘n teϺo<@?qY,,:60 Z(t)=g[X(t-1), X(t), Y(t-1), Y(t), Z(t-1)]. (1) Ïåðåìåííûå Z(t) îòëè÷àþòñÿ îò Y(t) òåì, ÷òî ïåðâûå íàáëþäàåìû ïî âûõîäíûì ëèíèÿì, à Y(t) â ýòîì ñìûñëå – âíóòðåííèå. Ôóíêöèîíàëüíûé ïîñëåäîâàòåëüíîñòíûé ïðèìèòèâ çàäàåòñÿ êîìïî- íåíòàìè: F 2 = <(t-1,t),(X,Z,Y),{A}>, ãäå (t-1,t) – äâà àâòîìàòíûõ ñîñåäíèõ òàêòà â îïèñàíèè ôóíêöèè; (X,Z,Y) – âåêòîðû âõîäíûõ, âíóòðåííèõ è âûõîäíûõ ïåðåìåííûõ; A – àëôàâèò îïèñàíèÿ ñîñòîÿíèé (ïåðåõîäîâ) àâòîìàòíûõ ïåðåìåííûõ [6,7]: A={0, 1, X={0,1},  }. Ôîðìîé îïèñàíèÿ ôóíêöèé ïðèìèòèâà ÿâëÿåòñÿ êóáè÷åñêîå ïîêðû- òèå C = (C 1 , C 2 , ..., C i , ..., C n ), (2) çäåñü C i = (C i1 , C i2 , ..., C ij , ..., C iq ) – êóá, âêëþ÷àþùèé âõîäíûå, âíóòðåííèå, âûõîäíûå êîîðäèíàòû C i = (C i X , C i Y , C i Z ), q=m+h+k. Äëÿ êîìáèíàöèîííîãî àâòîìàòà ôîðìàò îïèñàíèÿ êóáè÷åñêîãî ïîêðûòèÿ F 1 = <(t),(X,Z),{A}> îïðåäåëÿåòñÿ îòíîøåíèÿìè íà (q=m+k)-ìåðíîì âåêòîðå ïåðåìåííûõ C i = (C i X , C i Z ). Ôîðìàò çàäàåò ìíîãîâûõîäîâîé êîìáèíàöèîííûé ïðèìè- òèâíûé ýëåìåíò ñ m âõîäàìè è k âûõîäàìè. Äâîè÷íàÿ áóëåâà ôóíêöèÿ îò m ïåðåìåííûõ Z=f(X 1 ,X 2 ,..., X m ) îïðåäåëÿåòñÿ ïðè k=1. 3. Ôîðìóëèðîâêà ïðîáëåìû ìîäåëèðîâàíèÿ äîïîëíåíèé Ïðîáëåìà ìîäåëèðîâàíèÿ öèôðîâîãî óñòðîéñòâà ôîðìóëèðóåòñÿ â óñëîâèÿõ íåîïðåäåëåííîñòè îäíîãî èç êîìïîíåíòîâ ìîäåëè ) T , L , M ( W  , ãäå M – ìîäåëü, ïðåäñòàâëåííàÿ êóáè÷åñêèì ïîêðûòèåì C (2); L – êóáè÷åñêîå ïîêðûòèå ñïèñêîâ (ïðîâåðÿåìûõ) äîïîëíåíèé (ÊÏÑÄ) (Fault Lists Cubic Complement – FLCC); T – òåñò ïðîâåðêè öèôðîâîãî óñòðîéñòâà. Ïîêðûòèå äîïîëíåíèé äëÿ ïðèìèòèâà èëè öèôðîâîãî óñòðîéñòâà çàäàåòñÿ â âèäå: L= (L 1 , L 2 , ..., L i , ..., L n ), (3) çäåñü L i = (L i1 , L i2 , ..., L ij , ..., L iq ) – êóá, âêëþ÷àþùèé âõîäíûå, âíóòðåííèå, âûõîäíûå êîîðäèíàòû: i L = ) L , L , L ( Z i Y i X i , q=m+h+k; ) L , L ( Z ij Y ij = {0, 1, X}; 0 – îïðåäåëÿåò âû÷èòàíèå ñïèñêà ij L ; 1 – çàäàåò ïåðåñå÷å- íèå ij L ; X={0,1} – èäåíòèôèöèðóåò íåñóùåñòâåííîñòü ñïèñêà äîïîëíå- íèé ij L . 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Ïðèìåð 2. Çàäàíî êóáè÷åñêîå ïîêðûòèå ôóíêöèè 0 X 1 0 0 0 1 X 0 1 0 X 1 1 1 1 1 0 0 X Y X X X ) X X X X X ( С 3 2 1 3 2 1 3 2   . (9) Ñïèñêè èäåíòèôèêàòîðîâ äîïîëíåíèé äëÿ òðåõ âõîäîâ îïðåäåëåíû ïîäìíîæåñòâàìè: }. 7 , 4 , 3 , 1 { L }; 6 , 3 , 2 , 1 { L }; 5 , 4 , 2 , 1 { L 3 2 1    (10) Îïðåäåëèòü âûõîäíîé ñïèñîê äîïîëíåíèé äëÿ òåñò-âåêòîðà 1111. 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W;ږ{<ޒ$S9ݞm)OVi~[*)'038xghCY'ϗ7R89.{Lg*O+>UX [>~mO;r|䟭5Qd۾zUa^w>yW޷9f>fI{ApbW?N%ua|F c~MrpgKbp}Vj\]>6fkcw&v}@Q?! S[‰= k |4yWLXjmg>b=`#mA f9/_Ow>e$ ߏDǥ%+ G1+7>l|;[np!]R88]"$7Ho^{^ 0)7M񁾗qOyUG苍G8ܣ[m~ ;kI]'9IH_BNjGF=>嘃MNWؼ}?sr>SlOrp;LQrw_)9o@hHб*fgg4OÏ?~~r~ ^60ANSDlmek|fcaԖc r"9H6lwg~&3KTl_nA[(fN򰭫}cN_Stg=| >Yl~qNUʼTpLdA^2/U,,' 63 ). X X ( ) X X ( ) X X ( X X X X X X L 2 1 2 3 3 2 2 1 3 2 3 2           (11) Ïîäñòàâèâ âìåñòî ïåðåìåííûõ i X ñîîòâåòñòâóþùèå ñïèñêè i L , ïîëó÷èì ñëåäóþùèé ðåçóëüòàò: }. 7 , 6 , 5 , 4 , 2 { }) 6 , 3 , 2 , 1 { } 5 , 4 , 2 , 1 ({ }) 6 , 3 , 2 , 1 { } 7 , 4 , 3 , 1 ({ }) 7 , 4 , 3 , 1 { } 6 , 3 , 2 , 1 ({ L         (12) 4. Àëãîðèòì êóáè÷åñêîãî ìîäåëèðîâàíèÿ äîïîëíåíèé öèôðîâûõ ñõåì Ñ ïîìîùüþ (6) îïðåäåëÿåòñÿ àëãîðèòì êóáè÷åñêîãî ìîäåëèðîâàíèÿ äîïîëíåíèé ê òåñòó öèôðîâîãî óñòðîéñòâà (íà÷àëüíàÿ óñòàíîâêà íîìåðà âåêòîðà t=0): 1. Ìîäåëèðîâàíèå èñïðàâíîãî ïîâåäåíèÿ î÷åðåäíîãî ïðèìèòèâà ) M , 1 i ( P i  íà òåñò-âåêòîðå ) 1 t t ( T t   . Åñëè 1 N t   – ôîðìèðóåòñÿ ñïèñîê L(T) ïðîâåðåííûõ äîïîëíåíèé íà òåñòå T. Êîíåö ìîäåëèðîâà- íèÿ. Èíà÷å, 1 N t   – ïåðåõîä ê ï.2. 2. Åñëè âñå ýëåìåíòû ñõåìû îáðàáîòàíû ( ) i M  , âûïîëíÿåòñÿ ñðàâíåíèå âåêòîðîâ èñïðàâíûõ ñîñòîÿíèé ëèíèé â äâóõ ñîñåäíèõ èòå- ðàöèÿõ. Åñëè âåêòîðû èäåíòè÷íû 1 r t r t T T   , êîíåö ìîäåëèðîâàíèÿ t T è ïåðåõîä ê ï. 3. Èíà÷å – ïåðåõîä ê ï. 1. 3. Îïðåäåëåíèå ñïèñêîâ äîïîëíåíèé âíåøíèõ âõîäîâ êàê } j { L j T j  . Äëÿ íåâõîäíûõ ëèíèé óñòðîéñòâà âûïîëíÿåòñÿ ïðèñâàèâàíèå ) q , 1 m j ( L j     äëÿ ìîìåíòà t. 4. Ìîäåëèðîâàíèå äîïîëíåíèé ïðèìèòèâà ) M , 1 i ( P i  ïî ïðîöåäóðå (6). Äîáàâëåíèå ê ïîëó÷åííîìó ñïèñêó äîïîëíåíèÿ ê âûõîäíîé ëèíèè ïðèìèòèâà } j { j T . 5. Åñëè ïîñëå îáðàáîòêè âñåõ ïðèìèòèâîâ â äâóõ ñîñåäíèõ èòåðàöèÿõ âûïîëíÿåòñÿ óñëîâèå ) q , 1 j ( L L r j 1 r j    , îñóùåñòâëÿåòñÿ ïåðåõîä ê ï. 7. 6. Åñëè ïðè àíàëèçå ñîñåäíèõ èòåðàöèé ïðîâåðÿåìîå äîïîëíåíèå íà ëèíèè èñ÷åçàåò, òî åãî ñëåäóåò èñêëþ÷èòü èç ïðîöåäóðû ìîäåëèðîâàíèÿ òåêóùåãî âåêòîðà: )] L L ( ) L L [( r j 1 r j r j 1 r j q 1 j        . 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Áûñòðîäåéñòâèå îïèñàííîãî âûøå àëãîðèòìà ñêâîçíîãî èíòåðïðåòà- òèâíîãî ñèíõðîííîãî êóáè÷åñêîãî ìîäåëèðîâàíèÿ äîïîëíåíèé äëÿ îä- íîé èòåðàöèè èìååò îöåíêó }, 2 ] 3 ) Q 01 , 0 [( n q { W M 1 i 2 i i         ãäå i i q , n – ÷èñëî êóáîâ è ïåðåìåííûõ â ïîêðûòèè i С ; ) Q 01 , 0 (  – ñðåäíÿÿ äëèíà ñïèñêà äîïîëíåíèé äëÿ êàæäîé ëèíèè ñõåìû; Q – îáùåå ÷èñëî ëèíèé â öèôðîâîé ñõåìå; 2 è 3 – êîëè÷åñòâî èòåðàöèé àíàëèçà ïðèìèòèâà è ñõåìû ñîîòâåòñòâåííî. Ïðèìåð 3. Âûïîëíèòü ìîäåëèðîâàíèå îäèíî÷íûõ êîíñòàíòíûõ íå- èñïðàâíîñòåé ñõåìû, ïðåäñòàâëåííîé íà ðèñ.1. F1 F2 F1 F3 F1 1 2 3 4 5 6 7 8 9 1 2 3 4 5 Ðèñ.1. 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Äëÿ âõîäíîãî íàáîðà T= 1111 ìîäåëèðóåòñÿ èñïðàâíîå ïîâåäåíèå îáúåêòà, êîòîðîå äàåò âåêòîð (111101011). Çàòåì ãåíåðèðóåòñÿ ñïèñîê âõîäíûõ äîïîëíåíèé } j { L j T j  öèôðîâîãî óñòðîéñòâà: }. 4 { L }; 3 { L }; 2 { L }; 1 { L 0 4 0 3 0 2 0 1     Âûïîëíÿåòñÿ ïîñëåäîâàòåëüíàÿ îáðàáîòêà âñåõ ýëåìåíòîâ ñõåìû äëÿ âû÷èñëåíèÿ âûõîäíûõ ñïèñêîâ äîïîëíåíèé ñ ó÷åòîì (6). Äëÿ ïåðâîãî ïðèìèòèâà ðåçóëüòàò ìîäåëèðîâàíèÿ èìååò âèä }. 1 { L L 0 1 1 1 0 1 0 X 0 5 2 1 L 0 0 0 1 1 0 0 X 1 5 2 1 C ) 110 ( T L 0 2 1 1 F 5       Çàòåì ê ïîëó÷åííîìó ñïèñêó ñëåäóåò ïðèáàâèòü äîïîëíåíèå âûõîä- íîé ëèíèè, êîòîðîå èíâåðñíî ïî îòíîøåíèþ ê çíà÷åíèþ êîîðäèíàòû òåñò-âåêòîðà.  äàííîì ñëó÷àå ïîëó÷àåòñÿ ñïèñîê }. 5 , 1 { L 0 0 5  Ïîñëåäîâàòåëüíàÿ îáðàáîòêà îñòàâøèõñÿ ïðèìèòèâîâ â ñõåìå äàåò ñëåäóþùèå ðåçóëüòàòû: }; 6 , 3 , 2 , 1 { L 0 0 0 0 6  }; 7 , 1 { L 1 0 7  }; 8 , 6 , 5 , 3 , 2 , 1 { L 0 0 1 0 0 0 8  }. 9 , 7 , 4 , 1 { L 0 1 0 0 9  Êîëè÷åñòâî ïðîâåðÿåìûõ äîïîëíåíèé F ïî q ëèíèÿì ôîðìèðóåò îöåíêó êà÷åñòâà òåñòà (âåêòîðà): Q = [F/(2  q)]  100%. Äëÿ òåñò-âåêòîðà 1111 óïîìÿíóòàÿ îöåíêà ðàâíà: Q = [4/(2  9)]  100%= 22 %. Ïðèìåð 4. Âûïîëíèòü ìîäåëèðîâàíèå äîïîëíåíèé ê òåñòó ïîñëåäî- âàòåëüíîñòíîé ñõåìû, ïðåäñòàâëåííîé íà ðèñ. 2. Ôóíêöèè òðåõ òèïîâ ïðèìèòèâîâ ñõåìû îïèñàíû êóáè÷åñêèìè ïîêðûòèÿìè: 1 0 0 0 1 X 0 X 1 9 2 12 12 1 11 ) 1 F ( C ; S F X 0 1 E 1 0 0 E 0 0 0 X X 1 13 4 3 9 ) 2 F ( C ; Q J F X 0 J Q F X 0 0 1 E 1 0 1 0 E 0 0 1 0 X X 1 8 11 6 13 5 ) 3 F ( C ; 0 1 1 1 0 X 1 X 0 14 7 10 10 8 13 ) 4 F ( C . 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Äàëåå âûïîëíÿåòñÿ ìîäåëèðîâàíèå îäèíî÷íûõ äîïîëíåíèé äëÿ ïåð- âîãî âåêòîðà. Èñõîäíûå ñïèñêè ïðîâåðÿåìûõ äîïîëíåíèé âñåõ ëèíèé ñõåìû èìå- þò ñëåäóþùèé âèä: . L L L L L L }, 7 { L }, 6 { L }, 5 { L }, 4 { L }, 3 { L }, 2 { L }, 1 { L 13 12 11 10 9 8 1 7 1 6 0 5 1 4 0 3 1 2 0 1               Çàòåì âûïîëíÿåòñÿ ïåðâàÿ èòåðàöèÿ îáðàáîòêè âñåõ øåñòè ïðèìèòè- âîâ óñòðîéñòâà (ï. 4 àëãîðèòìà), êîòîðàÿ ïðåäñòàâëåíà ñëåäóþùèìè âû÷èñëåíèÿìè: }. 12 , 1 { 12 L L L 1 1 0 0 0 X 0 X 1 12 1 11 L 1 0 0 0 1 X 0 X 1 12 1 11 C 0 1 0 12 1 11 T 1 0 1 11 1 12 1 1 1        , F1 F1 1 2 3 F2 R D C R D C F3 4 5 6 F4 F4 1 2 3 4 5 6 7 12 9 13 11 8 10 14 Рис. 2. 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Cïèñîê ïðîâåðÿåìûõ äîïîëíåíèé íà âòîðîì âåêòîðå ïî íàáëþäàå- ìûì âûõîäàì ðàâåí }. 14 , 7 , 13 , 12 , 4 , 3 , 9 , 2 { L L L ) T ( L 0 1 0 1 0 0 1 0 14 13 12 2     Ðåçóëüòàò âûïîëíåíèÿ êóáè÷åñêîãî àëãîðèòìà ìîäåëèðîâàíèÿ äî- ïîëíåíèé íà âîñüìè íàáîðàõ ïîëíîãî ïðîâåðÿþùåãî òåñòà èìååò âèä 100 28 1 1 0 1 0 . . 0 . . . 1 . 1 89 25 1 1 1 . 0 . . 0 . . . 1 . 0 85 64 1 X 1 0 0 X 1 0 X 1 X 0 X . 85 53 1 0 1 0 0 1 1 0 X 1 X 0 0 . 67 42 0 0 1 . 1 1 0 . . 0 X 0 0 0 57 25 1 1 1 . 0 0 . 0 . . . . 1 . 39 32 0 0 1 . . 1 . 1 . . X 0 0 . 17 17 0 1 1 . . . . 1 . . . . . 0 (%) Q (%) Q 14 13 12 11 10 9 8 7 6 5 4 3 2 1 5 5 5 5 5 4 4 3 1 t  . Àëôàâèò îïèñàíèÿ òàáëèöû ïðîâåðÿåìûõ äîïîëíåíèé (ÒÏÄ) ij d D  îïðåäåëåí ñèìâîëàìè {0,1,X,  }. Îäíàêî ñóùåñòâóåò ñèòóàöèÿ äëÿ ïîñëåäîâàòåëüíîñòíûõ ïðèìèòèâîâ è ñõåì, êîãäà íà âåêòîðå i äëÿ ëèíèè j ïðîâåðÿåòñÿ äîïîëíåíèå, âîçíèêøåå íà íàáîðå r (r < i). 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Òî÷êà â ïðèâåäåííîé ÒÏÄ èäåíòèôèöèðóåò ïóñòîå ìíîæåñòâî ïðîâåðÿåìûõ íà ëèíèè äîïîëíåíèé. Ñòîëáåö t Q (  Q ) îïðåäåëÿåò ïðîöåíò ïðîâåðÿåìûõ (ïðîâåðåííûõ) íà âåêòîðå (òåñòå) äîïîëíåíèé. Ïðèìåð 5. Âûïîëíèòü ìîäåëèðîâàíèå äîïîëíåíèé äëÿ ñõåìû, ïðåä- ñòàâëåííîé ðèñ. 3, íà âõîäíîì íàáîðå 00 ïðè óñëîâèè, ÷òî ïðåäûäóùåå ñîñòîÿíèå ïî âõîäàì 1 è 2 ðàâíî 11. Ðåçóëüòàò èñïðàâíîãî ìîäåëèðîâà- íèÿ ñõåìû îïðåäåëÿåòñÿ â ñëåäóþùåì âèäå: 1 1 0 0 t 1 1 0 1 1 t 4 3 2 1 Line  . & 1 1 2 3 4 0 1 1 1 0 Ðèñ. 3. Ñõåìà ñ îáðàòíûìè ñâÿçÿìè Ðåçóëüòàò ìîäåëèðîâàíèÿ äëÿ íàáîðà 00 ïðåäñòàâëåí â âèäå èòåðà- òèâíîé ìàòðèöû 0 0 1 0 0 1 1 0 0 1 0 0 1 1 2 3 4 0 0 1 0 0 1 4 1 3 4 3 2 1 j 4 , 3 , 2 4 , 3 , 2 , 1 4 , 3 , 2 4 , 3 , 2 , 1 L L L 3 3 , 1 3 3 , 1 L L L I I I I L     ãäå ) 4 , 1 j ( I j  – ñòîëáöû èòåðàöèé, êàæäûé èç êîòîðûõ ñîäåðæèò ñïèñêè ïðîâåðÿåìûõ äîïîëíåíèé ïî âûõîäàì 3 è 4, êîòîðûå âû÷èñëÿþòñÿ ïî ôîðìóëàì, çàäàííûì â ñòîëáöå L j . Çäåñü íà ÷åòûðåõ èòåðàöèÿõ çàôèêñèðîâàí ãåíåðàòîðíûé ðåæèì äëÿ äîïîëíåíèÿ 1 1 íà âûõîäàõ 3 è 4, çàêëþ÷àþùèéñÿ â ðåãóëÿðíîñòè åãî ïîÿâëåíèÿ è èñ÷åçíîâåíèÿ.  ýòîì ñëó÷àå íåîáõîäèìî êîððåêòèðîâàòü ñïèñêè ïðîâåðÿåìûõ äîïîëíåíèé ïî ïðàâèëó ïóíêòà 6 êóáè÷åñêîãî àëãîðèòìà ìîäåëèðîâà- íèÿ. Äëÿ ïðèìåðà (ðèñ.4) óæå íà âòîðîé èòåðàöèè ñëåäóåò èñêëþ÷èòü èç ðàññìîòðåíèÿ äîïîëíåíèå 1 1 . Òîãäà âûïîëíåíèå èòåðàöèè I 3 äàåò îêîí÷àòåëüíûé ñïèñîê ïðîâåðÿåìûõ íà òåñò-âåêòîðå 0110 äîïîëíåíèé } 4 , 3 , 2 { L 0 0 1 4  . 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Òðèããåðíàÿ ñõåìà ìîäåëèðîâàíèå äîïîëíåíèé íà âåêòîðå 0111 òàêæå çàäàåò ãåíåðàòîðíûé ðåæèì ïî äåôåêòó 1 1 : 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 3 4 0 0 1 0 0 1 4 1 3 4 3 2 1 j 4 , 3 , 2 4 , 3 , 2 , 1 4 , 3 , 2 4 , 3 , 2 , 1 L L L 3 3 , 1 3 3 , 1 L L L I I I I L     Îêîí÷àòåëüíûé ñïèñîê ïðîâåðÿåìûõ íà òåñò-âåêòîðå 0110 äîïîëíå- íèé ñ ó÷åòîì êîððåêòèðîâêè èìååò âèä } 4 , 3 , 2 { L 0 0 0 4  . Çäåñü ôèçè÷åñêàÿ ïðè÷èíà èñêëþ÷åíèÿ 1 1 çàêëþ÷àåòñÿ â èíèöèèðî- âàíèè ðåæèìà ãåíåðàöèè íà ëèíèÿõ 3 è 4: 11-00-11-...-00. 5. Çàêëþ÷åíèå Ìåòîä êóáè÷åñêîãî ìîäåëèðîâàíèÿ äîïîëíåíèé ÿâëÿåòñÿ íîâîé òåõ- íîëîãèåé îáðàáîòêè öèôðîâûõ ñõåì âåíòèëüíîãî, ôóíêöèîíàëüíîãî, àëãîðèòìè÷åñêîãî óðîâíåé ïðåäñòàâëåíèÿ. Îí ïîçâîëÿåò çà îäíó èòåðà- öèþ ìîäåëèðîâàòü âñå äîïîëíåíèÿ ê òåñò-âåêòîðàì öèôðîâîãî óñòðîé- ñòâà. Óñëîâèå ïðèìåíåíèÿ çàêëþ÷àåòñÿ â íàëè÷èè òàáëè÷íîé ôîðìû îïèñàíèÿ ïðèìèòèâîâ öèôðîâîãî óñòðîéñòâà. Ïðåäëîæåííûé ìåòîä òàêæå ýôôåêòèâíî îáðàáàòûâàåò è ïîñëåäîâàòåëüíîñòíûå ïðèìèòèâû öèôðîâûõ àâòîìàòîâ, îïèñàííûå äâóõòàêòíûìè êóáè÷åñêèìè ïîêðû- òèÿìè [6,7]. Ïîñëåäíèå ôîðìàëèçóþò îïèñàíèÿ àëãîðèòìîâ â âèäå ïðèìèòèâîâ, ñîîòâåòñòâóþùèõ ãðàôàì ïåðåõîäîâ, ãðàô-ñõåìàì, òàáëè- öàì ïåðåõîäîâ öèôðîâûõ àâòîìàòîâ. Ìåòîä ðåàëèçîâàí â âèäå ïðîãðàììíîãî ïðèëîæåíèÿ è èñïîëüçóåòñÿ ïðè ãåíåðàöèè òåñòîâ äëÿ óñòðîéñòâ íà îñíîâå FPGA è CPLD. Êëàññ îáðàáàòûâàåìûõ ñòðóêòóð: êîíå÷íûå àâòîìàòû, îïèñàííûå â âèäå ãðà- ôîâ ïåðåõîäîâ, à òàêæå áóëåâû óðàâíåíèÿ ñ òðèããåðíûìè ñõåìàìè. Âõîäíîé ÿçûê îïèñàíèÿ öèôðîâûõ ñèñòåì – VHDL. Ïðîãðàììà ìîäå- }!xLUǟESHch@e6?05[s 64dkn9akkX"t`_JeK[$?\n.([ýw\ 3"F ռ8NVov i]=x6hyq! 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"77<<_}MJrK97۱ssrT%gGDhxUEa0 {¶v~(Àg{>) >Vﺸ~i/kܶh$q4y:S ⺥8yޡq.+Umܶj~FI(v|'g}"ΌGpLT>sSSt ssP|`-k<-χj>lp%v 5n9hM"(19G]ݮl2Uc=lV ˺W%%VMn;;_i>张D)ά.}?D^m\zLqkvR޿bܕoxUmlI7Se'Zs}J>a]Y@V>/#El}NƆ.ق9gs|g Ɗgv3)m^Ìƞ9kG?u紾ǣ>ei{ Jl ZuO mb}xTb8s&Qdy7tXoWHӷi5j},"q`=5AnQvuJt}hY^~/xX &;cw/}<7uXR'v)v/)?RxīʫqFH.҉Zת\#݊E؇[um^bVlr^+2w_<ݰeJm0@f}0oDkb?utOxy,b{:y=9oy?YKN;rܿ,q;R1g=O^xr'k'ZV<1F춭zCDdEyyx*nl[3qUa+i { kW(|C8)>ew؎Oi_ƫ޻Co_A>' 9P~q* &j*%Oάj,[m7P&lc"ŹW:fZ}:~RX`ƞxmcVG<xL[Rn}_Џexo $yz,?'2kނq'cݪ[ʢWƋT~ʼ^wmT1*6^ʱEMid4'RzGXEJEvjN_PllΪS|NJ7sç}'k_do|q|?"|O"xGS6VzPk`v'W+ |szw.$)Bz=ӗs܄.<<'<|t^`p ""7xaqiLlcs}~ռo8e1M6sA^5o'&onQm$7T#٣:b&"Fc4eZW.c)ۇ ΐJ}KV/4j(UK_z'yۚ<Z~%S:чCyN6}:92wXސw>"Zś,^wI{}ޒ%J/}fA_~'vaޭ&ؗ Yu}j >yY`X|f9^~/@7DuÔyƝ>D"7z"7kwdޫp CBa~!@prt@̯+'$Wd݉&>9g| ?~8(ĺA1 ~C.'F,h@4pxV̧U!-k A `5!nm?~v2rz`~!_%'˞VXNL|[:~r},x*f !h?X?@A3 }=}i[N|^ƛvCtG-SZ+;G<$Y[xv/}0oLyD? }cĝ:ľPה c,=ﳁm3M9c{^cr'&7GFۊ8X,fJ*N%MQ]9|lޛ=mxA?S*QXW &wGuqx^;1nS|c } 6+b6Y&,Vfd/O6iIq!*hg٫ LMBL-v⽺ p.mZQg(3jLY2fk2X[&ˌ3<8y<}ǰ=͆hf-&SMR`U^S%(d#$"w%G!,w03 ԑM_Ghp@%7w` ^nNSQ\͛`<6l0w v6s ?]km-#QKw eo.үʙ%cMkJoww@k͓?:Θ/~8 ϩϩ<- ΩPo{v -y_؃}n:x}- ~.g\7KfmҷSD?O_䴑ӆM3El)W˱yxIw(xo{Px"m?) | {R;<5lqOf s;c.čs.7uC"v*>/nx3[;KOku ;'d]'Ϙ}s|>sx BN:r=>6j(bou1UVKX[C>]{g~gC/.g0m3|[|δ/tUgZKc:7k9Ols8 r3/GƁL)>)ʆkSw-g7ě!^zz'_~ k>Fv_A;)B|ynNρ^z:vG❫>UqdϽ鯫-i:N/,lr|c)9^OqجC -cuE̶(.W{M̞[}bvd~?;秞g2l7de3C?!7N7y|>8x -ۮ\+_9Z6C瞪OsgDs?_{L,,o 72 ëèðîâàíèÿ äîïîëíåíèé îðèåíòèðîâàíà íà èíòåãðàöèþ â ñèñòåìû ïðîåê- òèðîâàíèÿ ôèðì: Aldec, Xilinx. Ñïèñîê ëèòåðàòóðû: 1. Åðìèëîâ Â.À. Ìåòîä îòáîðà ñóùåñòâåííûõ íåèñïðàâ- íîñòåé äëÿ äèàãíîñòèêè öèôðîâûõ ñõåì. Îáùèå âûðàæåíèÿ äëÿ íåèñïðàâíî- ñòåé, âîçìîæíûõ ïðè ýêñïåðèìåíòå // Àâòîìàòèêà è òåëåìåõàíèêà, 1971. ¹ 1. Ñ. 159-167. 2. Armstrong D.B. A deductive måthod of simulating faults in logic circuits. IEEE Trans. on Computers. 1972. Vol. C-21. No. 3. P. 464-471. 5. Áèðãåð À.Ã. Ìíîãîçíà÷íîå äåäóêòèâíîå ìîäåëèðîâàíèå öèôðîâûõ óñòðîéñòâ // Àâòî- ìàòèêà è âû÷èñëèòåëüíàÿ òåõíèêà. 1982. ¹4. Ñ.77-82. 4. Levendel Y.H. and Menon P.R. Comparison of fault simulation methods – Treatment of unknown signal values. Journal of digital system. 1980. Vol.4. P.443-459. 5. Abramovici M., Breuer M.A. and Friedman A.D. Digital System Testing and Testable Design, Computer Science Press, 1998. 652 p. 6. Hayes J.P. A systematic approach to multivalued digital simulation// ICCD-84: Proc. IEEE Int. Conf. Comput. 1984. No. 4. P. 177-182. 7. Õàõàíîâ Â.È. Òåõíè÷åñêàÿ äèàãíîñòèêà ýëåìåíòîâ è óçëîâ ïåðñîíàëüíûõ êîìïüþòåðîâ. Ê.: IÇÌÍ. 1997. 308 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 23.06.2000 Õàõàíîâà Èðèíà Âèòàëüåâíà, êàíä. òåõí. íàóê, äîöåíò êàôåäðû àâòîìàòèçàöèè ïðîåêòèðîâàíèÿ âû÷èñëèòåëüíîé òåõíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: òåõíè÷åñêàÿ äèàãíîñòèêà âû÷èñëèòåëüíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40- 93-26. E-mail: Hahanov@Kture.Kharkov.ua Ïóäîâ Âèòàëèé Àíàòîëüåâè÷, àñïèðàíò êàôåäðû àâòîìàòèçàöèè ïðîåêòèðîâàíèÿ âû÷èñëèòåëüíîé òåõíèêè ÕÒÓÐÝ. Íàó÷íûå èí- òåðåñû: òåõíè÷åñêàÿ äèàãíîñòèêà âû÷èñëèòåëüíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 40-93-26. ×àìÿí Àéê Ëåâîíîâè÷, àñïèðàíò êàôåäðû àâòîìàòèçàöèè ïðîåêòè- ðîâàíèÿ âû÷èñëèòåëüíîé òåõíèêè ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: òåõíè÷åñêàÿ äèàãíîñòèêà âû÷èñëèòåëüíûõ ñèñòåì. Àäðåñ: Óêðàè- íà, 61166, Õàðüêîâ, ïð. 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ËÈÇÃÈÍ ÐÀÑÏÐÅÄÅËÅÍÍÛÅ ÔÎÊÓÑÈÐÓÞÙÈÅ ÔÀÊÒÎÐÛ È ÍÅÊÎÒÎÐÛÅ ÈÕ ÏÐÈÌÅÍÅÍÈß Ôîðìóëèðóþòñÿ óñëîâèÿ ôîêóñèðîâêè ïðè âîçäåéñòâèè íà ìàðêîâñêèé ïðîöåññ ñ íåïðåðûâíûì âðåìåíåì ôîêóñèðóþùèõ ôàêòîðîâ, íåêîòîðûì îáðàçîì ðàñïðåäåëåííûõ íà âðåìåííîì îòðåçêå. Ðàññìàòðèâàþòñÿ íåêîòîðûå ïðàêòè÷åñêèå çàäà÷è, ðå- øåíèå êîòîðûõ ìîæåò áûòü ïîëó÷åíî ñ ïðèìåíåíèåì äàííîé ìåòîäèêè.  ðàáîòàõ [1-3] ñôîðìóëèðîâàíû óñëîâèÿ, ïðè âûïîëíåíèè êîòîðûõ èìååò ìåñòî ôîêóñèðîâêà âåðîÿòíîñòåé ñîñòîÿíèé íåîäíîðîäíîãî ìàð- êîâñêîãî ïðîöåññà ñ äèñêðåòíûì ìíîæåñòâîì ñîñòîÿíèé è íåïðåðûâ- íûì âðåìåíåì íà çàäàííîå ðàñïðåäåëåíèå. Îñíîâíûìè óñëîâèÿìè, êîòîðûå ïðèâîäÿò ê ôîðìèðîâàíèþ ôîêóñèðóþùåãî ýôôåêòà, ÿâëÿþò- ñÿ áûñòðî èçìåíÿþùèåñÿ âî âðåìåíè ôàêòîðû, âûçûâàþùèå ñèëüíûå âîçìóùåíèÿ ýëåìåíòîâ èíôèíèòåçèìàëüíîé ìàòðèöû   t  èññëåäóåìîãî ïðîöåññà. Ñôîðìóëèðóåì ýòè óñëîâèÿ [3]. 1. Ïóñòü ñóùåñòâóåò òàêàÿ ïîñëåäîâàòåëüíîñòü ïîïàðíî íåïåðåñåêà- þùèõñÿ èíòåðâàëîâ       1 , k k k t s , 1    k k k s t s , 0 t s k  ,   0 t è òàêàÿ ïîñëåäîâàòåëüíîñòü èíäåêñîâ k j (  , 2 , 1  k ), äëÿ êîòîðûõ   0 inf 1       k t s ij k k k ds s (1) íà ìíîæåñòâå        1 0 0 , \ , k k k t s t s , (2) à íîðìà ìàòðèöû   s  îãðàíè÷åíà îäíîé è òîé æå êîíñòàíòîé: C   . 2. Ìàòðèöà   t  íåïðåðûâíà íà îòðåçêàõ   k k t s , è ñóùåñòâóåò ïðåäåë   p p k k       lim . (3) Çäåñü   k k k t s ,   ,   k p   – íóëåâîé ñîáñòâåííûé âåêòîð ìàòðèöû   k    (çíàê * îçíà÷àåò îïåðàöèþ òðàíñïîíèðîâàíèÿ). x}LUuǟA.G=P4PAaJK-˵5#-KsMךk8{Y\J4Q&**Ђ|Y[aV˅܄˭={~9_BDI"*298Dl͉g*u= 4{ N;TFyԃCVՄ,Ը8IS,Ԯ}8_R7~|g[kBU}n,9 .}4 |zЮO}Am;#6U;Zc >hr(?t4v\6Y#fK_Ӑ/5mFWW6S,okgq߶CXǻ!H7/U~:Ut9pwYk2 t#WcW4z揂F_)a>P,#1nGcc|[r7p3OA>=UӇdoDe9lT@)wrEؔ]'h]NƅVZtP6w? 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( 2ziw_RxO7!G=V8x_~B6mY a~sC=vhj.tEvR"Gէ=vv^ }AxBwm61_ʆ}o1 рeԺ<˗/wz_8 O帷HeymR{5ywƷt=bo!ypÂxPoiVc<`su;-Ug]u7_{ f>_t m ~sױKy4SyAY~Y,2Yr_6>eDJ7dhǺh:7&c0iԛ~Io'OO@zWBD]k,Co8iY񎯝),k>6^@ُ?.}K9l#mFB3Fpi끟`'Oz\.aGxK(4֣5!4Gu&F-hNPy89zn5Cf)}W2k% N@.av%+m~?u:\ q ayCa]m?gɽH.yScS})K̲ߗފlCz-5~ N z[h5VhFUڝ󜦿z\_VlJo(={ˏN)mȥgivN',5~B1?oV 9Ϟ4*r 9tf7@<.oЂ6O{ 8MC~/Ck1iq0ڒ|қ.H]>~5"vOBe)~![6~T6QA]q64`go2 8y1ޮ2 LX|{G1~/ƾդg=H9˼ /H^ҹl5M[ԛ1A9)`O]i 3pI3"x(酪(sBMnH<>8ds Nij'c`_̶DopEK#681 dw\aSrȿ-N}XceeXOܿ Cn_~4M{Dă'#aL_#{x܁@F\.eSG%iB߁dz ZpG+-{SZHN6ЦǚL7}8> ZjkGܨ o{\^O  XwekZӓS#ʟgQtER?Wj[4w${=*`]B }{vyu[Gk}p\vU']ͅB?Kٰ Tol-ָ!4 ʀ#<8x: kۄ d/,gu[2$,vIiO4b{<DǏ< m#,$=a5d'88=sr[+@ޫ*w\u :Ӻ虍^V^}NxP|@.EOWA^ (s^{o)yu[jx=*$0Omu98Kj^xW٭FU7L;SOU]o51_ʆ*>[ɫ4`(\'aAxY^+dVl8K#4YcaŸUr)`\KwSOs4ܱlS Ȱ> Wq,^ H߲04IGy%Lz0cD:e.)x.qie5$~b:2?qh];,,74 Òîãäà äëÿ ëþáîãî j (èíäåêñ j íóìåðóåò ñîñòîÿíèÿ) è ëþáîãî íà÷àëüíîãî ðàñïðåäåëåíèÿ âåðîÿòíîñòåé, çàäàííîãî â òî÷êå 1 0 s s  ,   j j t s p s s p   , lim 0 0 , (4) ãäå j p - j -ÿ êîìïîíåíòà âåêòîðà ðàñïðåäåëåíèÿ âåðîÿòíîñòåé p  èç (3).  îïèñàííîé ñèòóàöèè 0 t íàçûâàþò òî÷êîé ôîêóñèðîâêè. Åñëè ðÿä (1) ñõîäèòñÿ, íî ñóììà åãî äîñòàòî÷íî âåëèêà, òî, íà÷èíàÿ ñ íåêîòîðîãî 0 k , âñå ðàñïðåäåëåíèÿ   k p   , ( 0 k k  ) èç (3), íà êîòîðûå ôîêóñèðóåò ïðîöåññ â òî÷êàõ k t , ñîäåðæàòñÿ â   -îêðåñòíîñòè ïðå- äåëüíîãî ðàñïðåäåëåíèÿ p  è 0 t ÿâëÿåòñÿ òî÷êîé  -ôîêóñèðîâêè. Çäåñü     inf ,   – ëþáàÿ îêðåñòíîñòü ðàñïðåäåëåíèÿ p  , ãäå íà÷è- íàÿ ñ íåêîòîðîãî 0 k , ñîäåðæàòñÿ âñå   k p   . Ïðîñòåéøèé íàáîð óñëîâèé, îáåñïå÷èâàþùèé ôîêóñèðîâêó ðàñïðå- äåëåíèé ïðîöåññà ñ èíôèíèòåçèìàëüíîé ìàòðèöåé   s  ( 0 0 t s s   ) â òî÷êå 0 t , òàêîâ. Ñóùåñòâóåò ñòîëáåö 0 j ìàòðèöû   s  , äëÿ ýëåìåíòîâ êîòîðîãî âûïîëíÿþòñÿ óñëîâèÿ: 1.       0 0 inf t s ij i ds s , (5) íèæíÿÿ ãðàíü áåðåòñÿ ïî âñåì çíà÷åíèÿì i . 2. Ñóùåñòâóåò   p s p t s     0 lim . Çäåñü   s p  – íóëåâîé ñîáñòâåííûé âåê- òîð ìàòðèöû   s   . Òîãäà 0 t ÿâëÿåòñÿ òî÷êîé ôîêóñèðîâêè è èìååò ìåñòî (4). Åñëè æå íèæíÿÿ ãðàíü â (5) êîíå÷íà, íî äîñòàòî÷íî âåëèêà, òî 0 t åñòü òî÷êà  -ôîêóñèðîâêè. Ñëó÷àé ôîêóñèðîâêè (òî÷íàÿ ôîêóñèðîâêà) èìååò ìåñòî, åñëè âû- ïîëíÿåòñÿ (1) (èëè (5)). Îí ìîæåò áûòü ðåàëèçîâàí ëèøü ïðè áåñêîíå÷- íûõ ýíåðãîçàòðàòàõ.  ñëó÷àå òî÷íîé ôîêóñèðîâêè è  -ôîêóñèðîâêè ñðåäè ýëåìåíòîâ ìàòðèöû   s  åñòü ýëåìåíòû, êîòîðûå ïðè 0 t s  áûñò- ðî âîçðàñòàþò. Òàêîé ðîñò îáû÷íî âîçíèêàåò èç-çà âîçäåéñòâèÿ íà ïðîöåññ áûñòðî èçìåíÿþùèõñÿ ôàêòîðîâ, ëîêàëèçîâàííûõ ÷àùå âñåãî íà ìàëûõ ïðîìåæóòêàõ âðåìåíè. ×àñòî áûâàåò, ÷òî òàêèå ôàêòîðû, ìíîãîêðàòíî âîçäåéñòâóÿ íà ïðîöåññ íà íåêîòîðîì ïðîìåæóòêå âðåìå- íè, âñÿêèé ðàç âûçûâàþò ñèëüíûå “ ïî÷òè íåèíòåãðèðóåìûå ” âîçìóùå- íèÿ ýëåìåíòîâ ìàòðèöû  , ÷òî ïðèâîäèò ê ìíîãîêðàòíîìó ïîÿâëåíèþ òî÷åê  -ôîêóñèðîâêè. 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Òàêèå ôàêòîðû íàçûâàþò ôîêóñèðóþùèìè [5].  ýòîì ñëó÷àå äëÿ âñåõ èçìå- ðèìûõ ïî Ëåáåãó ìíîæåñòâ èç   b a, ìîæíî ââåñòè ìåðó F ôîêóñèðîâ- êè. Äîñòàòî÷íî ââåñòè ýòó ìåðó íà ìíîæåñòâå âñåõ ïîëóèíòåðâàëîâ     b a t t , ,     . Ïîëîæèì         t t r t t R t t F j j j            , , sup , , (6) ãäå     t t p t t R ij i j        , sup , ,     t t p t t r ij i j        , inf , ,   t t p ij    , – ïåðåõîäíûå âåðîÿòíîñòè. Òàêèì îáðàçîì, âåëè÷èíà   t t F    , èç (6) îïðåäåëÿåò ñóììàðíûé ôîêóñèðóþùèé ýôôåêò, âîçíèêàþùèé çà ñ÷åò âñåõ òî÷åê ôîêóñèðîâ- êè, “ ðàçìàçàííûõ ” íà   t t    , . Åñëè òî÷åê ôîêóñèðîâêè íà   b a, äîñòàòî÷íî ìíîãî è âêëàä êàæäîé èç íèõ â ñóììàðíûé ôîêóñèðóþùèé ýôôåêò íà   b a, ìàë, ìîæíî ââåñòè ïîíÿòèå ïëîòíîñòè ðàñïðåäåëåíèÿ   t p F òàêèõ òî÷åê íà   b a, . Ïðè ýòîì ñëåäóåò èñïîëüçîâàòü ìàêðîñêîïè÷åñêîå îïèñàíèå ïîíÿòèÿ ïëîòíîñòè (ñì., íàïðèìåð, [4]), êîãäà ïðåíåáðåãàþò “ ìèêðîñêîïè÷åñêè- ìè ” çíà÷åíèÿìè óñðåäíÿåìûõ âåëè÷èí. Åñëè ñðåäè òî÷åê ôîêóñèðîâêè åñòü òî÷êè, âêëàä êîòîðûõ â ñóììàðíûé ôîêóñèðóþùèé ýôôåêò ñóùå- ñòâåíåí, ïðè îïèñàíèè ïëîòíîñòè   t p F ñëåäóåò èñïîëüçîâàòü  -ôóíê- öèè.  ñëó÷àå, êîãäà ïëîòíîñòü ôîêóñèðîâêè   t p F ïîñòîÿííà íà   b a, äëÿ ëþáîãî     b a t t , ,     , ìåðà   t t F    , çàâèñèò ëèøü îò ðàçíîñòè t t     è íà ëþáîì   t t    , ôîêóñèðîâêà ïðîèçâîäèòñÿ íà îäíî è òî æå ðàñïðåäåëå- íèå. Îïèñàííûå âûøå ôîêóñèðóþùèå ôàêòîðû îáû÷íî äåéñòâóþò íà ôîíå íåêîòîðîé ñòîõàñòè÷åñêîé (èíôèíèòåçèìàëüíîé) ìàòðèöû, êîòî- ðàÿ îò íèõ íå çàâèñèò. Òàêèå ìàòðèöû áóäåì íàçûâàòü ôîíîâûìè. Åñëè âîçìóùåíèÿ, ïîðîæäàþùèå ôîêóñèðóþùèå ôàêòîðû, ëîêàëèçîâàíû íà ìàëûõ ïðîìåæóòêàõ âðåìåíè   t t t   , è íîðìà ôîíîâîé ìàòðèöû íåâå- ëèêà, òî åå âêëàä â ïðîöåññ ôîêóñèðîâêè íà   t t t   , ìàë. Ðàññìîòðèì ïðîñòåéøèé ñëó÷àé ðàñïðåäåëåíèÿ ôîêóñèðóþùèõ ôàê- òîðîâ íà   b a, , êîãäà îíè ñîñðåäîòî÷åíû íà ðàâíîîòñòîÿùèõ äðóã îò äðóãà íåïåðåñåêàþùèõñÿ èíòåðâàëàõ   i i i t t t   , , ( n i , , 1   ). 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Ìíîæåñòâî âñåõ âîçìóùåííûõ ñîñòîÿíèé ïîðîæäàåò èíôèíèòåçèìàëüíóþ ìàòðèöó, êî- òîðóþ íàçûâàþò ôðàãìåíòîì. Ïðåäïîëàãàåòñÿ, ÷òî ïåðåñåêàþùèåñÿ ôðàãìåíòû îïðåäåëåííûì îáðàçîì ñîãëàñîâàíû ìåæäó ñîáîé [3]. Åñëè óñëîâèÿ ñîãëàñîâàíèÿ âûïîëíåíû, òî ïðè íåêîòîðûõ åñòåñòâåííûõ îãðàíè÷åíèÿõ íà ïîñëåäîâàòåëüíîñòü ìîìåíòîâ âðåìåíè, êîãäà ïðîèñ- õîäÿò âîçìóùåíèÿ, ïðîöåññ ñòàáèëèçèðóåòñÿ: âåðîÿòíîñòè åãî ñîñòîÿ- íèé ñ ðîñòîì âðåìåíè ëèáî ïðèíèìàþò íåêîòîðûå ïðåäåëüíûå çíà÷å- íèÿ, ëèáî ëîêàëèçóþòñÿ âáëèçè íèõ. Ðåàëèçàöèÿ ïðîöåññà ñòàáèëèçàöèè â êàæäîì êîíêðåòíîì ñëó÷àå òðåáóåò ïðîâåäåíèÿ ïðåäâàðèòåëüíûõ èññëåäîâàíèé. Ïóñòü, äëÿ îïðåäå- ëåííîñòè, ðå÷ü èäåò î òàêèõ âîçäåéñòâèÿõ íà ïðîöåññ ðàñòâîðåíèÿ òâåðäûõ ïðèìåñåé â æèäêîé ñðåäå, ïðè êîòîðûõ ê ìîìåíòó âðåìåíè 0 t ñêîðîñòü ðàñòâîðåíèÿ òâåðäîé ïðèìåñè k П ,  , 2 , 1  k äîëæíà áûòü ðàâíà k V . Òîãäà, çíàÿ ìàññó êàæäîé ðàñòâîðÿåìîé ïðèìåñè k П , ìîæíî íàéòè åå îòíîñèòåëüíóþ ïëîòíîñòü k p âî âñåì ðàñòâîðå ê ìîìåíòó 0 t . Íà ïðàêòèêå îïèñàííûé ïðîöåññ ÿâëÿåòñÿ ëèøü ÷àñòüþ íåêîòîðîãî òåõíîëîãè÷åñêîãî ïðîöåññà, è òðåáóåòñÿ âûáðàòü òàêèå âíåøíèå âîçäåé- ñòâèÿ íà íåãî, ÷òîáû â ìîìåíòû 0 t t  îòíîñèòåëüíûå ïëîòíîñòè   t p k ïðèíèìàëè çàäàííûå çíà÷åíèÿ   t p k , íàïðèìåð, íå èçìåíÿëèñü:   k k p t p  .  òàêîé ñèòóàöèè ïðèõîäèòñÿ ðåøàòü íåñêîëüêî çàäà÷. Ñëåäóåò ðàçáèòü ðàáî÷åå ïðîñòðàíñòâî D , â êîòîðîì ïðîèñõîäèò ðà- ñòâîðåíèå, íà íåñêîëüêî ÷àñòåé k D , â êàæäîé èç íèõ ðàñïîëîæèòü èñòî÷íèêè âîçìóùåíèé, ïîðîæäàþùèå ôîêóñèðóþùèå ôðàãìåíòû. Ýòè èñòî÷íèêè ñëåäóåò âûáðàòü òàê, ÷òîáû âûïîëíÿëèñü óñëîâèÿ ñîãëàñîâà- íèÿ èç [3] è ÷òîáû ïðè 0 t t    t p k ïðèíèìàëè çàäàííûå çíà÷åíèÿ (èëè ìàëî îòëè÷àëèñü îò íèõ). Ðàçáèåíèå ðàáî÷åãî ïðîñòðàíñòâà íà îáëàñòè k D ìîæåò áûòü ïðîèçâåäåíî ìíîãèìè ñïîñîáàìè. Çäåñü âîçíèêàåò çàäà÷à îá îïòèìàëüíîì âûáîðå îáëàñòåé k D . Åñëè ìîìåíò 0 t ôèêñèðî- âàí, òî ñòàâèòñÿ çàäà÷à î òàêîì âûáîðå k D , ïðè êîòîðîì ðåàëèçàöèÿ ïðîöåññà ñâÿçàíà ñ ìèíèìàëüíûì ðàñõîäîì ýíåðãèè. Ðå÷ü ìîæåò èäòè òàêæå î òàêîì âûáîðå k D , ïðè êîòîðîì äëÿ ôèêñèðîâàííîãî îáúåìà ýíåðãîçàòðàò è çàäàííîì íà÷àëüíîì ìîìåíòå ïðîöåññà ðàñòâîðåíèÿ 0 s ðàçíîñòü 0 0 s t  ïðèíèìàëà ìèíèìàëüíîå çíà÷åíèå. Ñ èçìåíåíèåì âðå- ìåíè ôèçè÷åñêèå õàðàêòåðèñòèêè ðàáî÷åé ñìåñè èçìåíÿþòñÿ, â ñâÿçè ñ ÷åì òðåáóåòñÿ îïðåäåëåííûì îáðàçîì èçìåíèòü ìîùíîñòè èñòî÷íèêîâ âîçìóùåíèé â êàæäîé îáëàñòè k D . Ýòè èçìåíåíèÿ âûáèðàþòñÿ òàê, ÷òîáû ñîîòâåòñòâóþùèå ýíåðãîçàòðàòû áûëè ìèíèìàëüíû è îñíîâíûå ðàáî÷èå õàðàêòåðèñòèêè ïðîöåññà ìàëî îòëè÷àëèñü îò ïàñïîðòíûõ. Èç ïåðå÷èñëåííûõ çàäà÷ âèäíî, ÷òî óïðàâëåíèå ïðîöåññîì ðàñòâîðåíèÿ &xilTU{m3 EBE#%DY BH?fXF4D!,*R6w@CDe | /6sf$&&~xM==;އ+ԈHyH_+,h.'U%P_ F/27Ag# u;wzjwnA6,y0̎{r[۲ߖS$rҏj.R.me\+_y_,SnTvERJTį"ъ],q3o}5sTPaSmAb "rT7ITZ>$s.nxDvH_JGIygv/ݸ ~;)y(L϶;&9 D􊬎qT:fmdkOs&2y8+TJVyd4JUZɛ-Y{Hp[k_-.{Ҙltʶ>_YZ#L{;wgd~tvl̡ya:r`G]~D[;NS-IM<'>YsfvԞص/v?L|yum_-=0k5lc/blb*O>S֪}35yΉFO؁d΋*޻}堌xɓ=+/ur=ɓ~g/2)8a➄'[&nJK'P@Q8Fl; z,A&2x c Լ ~9g (" 0my2 %]86{}+]x,x1{Ùo ̽,2:#WLڧ 2LD9n<}t "\_xȾz6ɽ)FS _BT&r>Y<[wJMx?x ysxYy{@8o=l4&?GK?.{:K!Y7w]}{'uUG'.ŕҝ\*}l%f(* Le.oa|܀.p[#$~ C2{FH$O-SlKkǁ6ϣb)OлG*tzo7tqj/lT뿭̧@#gbs7gήq{˖;i&m3m ʙz aߍU꾮&G*~G|SAY7lu*gzA_wJ*}XIUl-=V9Tgj4Q3N6.2>8؟tL~9ȦLpoJ0>2$ZK&/@؁a;v et a;v ]EMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:29     0  (16&2.'/ 1 4Y{XxŜuˏ]TZn mmlS'01VLt)dZ3v0k3 )A@@VdY]]D${}I|9{9{ޗJNB Bwycn z'/6:7 uDžoC3*@g. 7k P|>|YLo\\`C*aW4(OR* 4Im& ~Ȍ`)*O,TTyFP-*a~GXĢ Lpv1g 3M>ںHxE/֡nGz#rQۙ^i-0.Ň Lx "Ϲ|ȹϖA_mjAs;ssօ~ס]?SrG>e>j$Q04 *|RNYEk%~+ƶ>&O' 7όSI,/ >uuo+wB'43-KW`DW^rd#喇FMl=ynAV@nY#s< \oWar'ߩ:m70~ {H6րFkO#8OP)\$vPW޸k}7ss7y2=`N5?gO2eGưAP;x1=0G+T5IۼRv{5G{(he^YO}Zmۀ#>?ftl'~o[Povțo*=/w;Dz b\U*賤vd->L'{c/,ၱl'l>BG:2ďcV_>'VfdN;Nl5]*Y#L=hc$4S:}ma83r/֫X"f [䧧Tz^5o96[O3Ɩԅ-h%rm.~}y >h?mMc1hfx]vp^s[;jm[!]eX+31;ݲKUkܢأ^֫*%K;\Ijب5cq3^؊XE)eǔ^.IPexw%k6Hrâ](ZM_o{Oksgd}mL#_7sx&U昗RV?~c%nڏ`@ۡs9tЇ@y+Ǐ>WD[,2oOȻq%nSo_JZ˹y'$^!Ɂ^ t8Fln`3-zz 34'd2r<{.l9yv~V'e^{/oYBq8?~ŜwGJ.G_Yfwv`]oiA9~7ϐ|N" PclSkq39S"z%څ;4^l:DuxkDpw<~\M%u Bvۣw No6?% ɖxxsoܡG0_euF)O5UJP\9 26 183U:y5< ;)zTu5)Sce1clWW ?6wg{\6sgT^UIq|:Ua媿mhe}xTmK򮌯3'\<+2 TƷ~.uqnq?y[ρ$|/ֈX H|A bxek6b ̸&~O ߣ~5y) |~n!ӗq~bܧ6Ao%`;aaEXjmvcxn<;4#<;ux^lM큡:ReЅ,h nCSwfF& YC>~w~k8{k؄l:}T\QjR_w0L ԭO t^63caf6!4ll#G"g>>ȣ>s}hnLuS}7*_,|sHhD+zۜT^7[J^7>ɫq.7]zb/n6w⭢[{t$mmby|+Q6/ϖiuG'6r]aqC}~x'b!g<_ WU_c8?Oq7 xF> ;',w n%wjwr:p8m}C |M>14a'ld_7 %g|Cޯq&L uS)]*?OD95,|̖ʬ s y[O3^b;6`Nnζ74/C6PtheNÌz)\{<m5oY|{&o5 / Zwx 6],wg'kudZx%zA7wvw$\vg{WU.-C}FM!Tq*lJ]O9˧T/`^%^ufF`nC(5M\Mڰ<Цgqwk/%a{kEc~,䟘}:8Ͷ5;cg` Ro^/}F)<;Bkh ̉%]n,:wqsKb>a`H>n=#tac*cvrAڍǎwXt1zAc> LjGKɿnobvj*}p?{ WZ=S_4HGSf;+*."V Z&7I+z~JYCUQSÄz*}O< >c78K+i~su }/; _oo~n kF5mn 2ao*aЙm4s%u͔RA܇{N͸n=tth6T7)o;«zW*>t%ڕ''yk7fXr{o##StШ7C{Cd]2-L zM`Mm;|'c^'"f/ P>ʢ&73ϔ٣0iv_=C ~~weqY%ݝ_=/`Nr)z;QMr #_,UZ.1B'83"֦i^+RPk,~/5wjޣ6hf9mōzbHzڮ WCM||cNɞ'uyClM)ts[T6Lx&>6޵_g{&P3Iel/2j;Գo,u탏m:e m`{ڱCj6s/7~:~Q{g,>$|7~I~~|~u@_sJK%N(! OvkC8 2340%S[5 9hĀee=mu)S:~)~y_/"ɖ͗ќζ^StS}x>8퇥#pPtKtr 3 q2VȰy`= y!y|g'':1ҷ\Hu;jZd;v`{ll[эn҆:Q6[7Ü㽙zUwуoo䛽oNV4o|.vj./=}Z׹JsLE㻓n4iqdǚ?99|-f.^mg`S3o[q=և,ϴ>! _]#r[4 l-2ۛ.Yz,XoA6zgإLs, ;`bl䶃γmwCGѾ 2-\f]ZMem˹U'2m' _yv'Mfe 2O3wI"$՘CkxtG ]Su|5ΕlSx}{x~woB'/^NYMa|Q[7 @"|0ϲ+erd,`Aa|Yf5N։Gn&v)͊(ѲdmK(qx}tg04yf|<3v1[Y2cc>sy#@>35F39oh7g;'H@v ` lHCcFQ2gK}W|x`htCR&fԇo}ԃ8{_W gDdfo?闄 |irƿ|7\v.ӢtD.$m02{/2û[P;pO>m\|f䶄`K􍵏C|[}~XѼ]Ѱqxozη _27ݶۥ\'`,⪖=|>ze9,,79 òðåáóåò ïðîâåäåíèÿ äîïîëíèòåëüíûõ èññëåäîâàíèé è ðåøåíèÿ ðÿäà âñïîìîãàòåëüíûõ çàäà÷. Ñïèñîê ëèòåðàòóðû: 1. Äèêàðåâ Â.À. Òî÷êè ôîêóñèðîâêè è òåîðåìû î ñóùå- ñòâîâàíèè ïðåäåëüíûõ âåðîÿòíîñòåé. Õàðüêîâ, 1995. 9 ñ. Äåï. â ÃÍÒÁ Óêðàè- íû 28.02.95, ¹ 526 – Óê95. 2. Ãåðàñèí Ñ. Í., Äèêàðåâ Â. À., ×èñëèí Í. È. Ñóùåñòâîâàíèå ïðåäåëüíûõ âåðîÿòíîñòåé äëÿ êîíå÷íûõ ïðîöåññîâ Ìàðêîâà ñ óáûâàþùèìè ê íóëþ âðåìåííûìè ïðîìåæóòêàìè ïåðåõîäà // Äîïîâ³ä³ ÍÀÍ Óêðà¿íè, 1998. ¹7. Ñ. 15-19. 3. Äèêàðåâ Â. À. Ëîêàëüíûå âîçìóùåíèÿ è ôîêóñèðîâêà ðàñïðåäåëåíèé ìàðêîâñêèõ ïðîöåññîâ // Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. 1999. ¹ 4(09). Ñ. 37–39. 4. Ëàíäàó Ë. Ä., Ëèôøèö Å. Ì. Ýëåêòðî- äèíàìèêà ñïëîøíûõ ñðåä. Ì.: Íàóêà, 1985. 230 ñ. 5. Äèêàðåâ Â. À. Ôîêóñèðîâêà ðàñïðåäåëåíèé ìàðêîâñêèõ ïðîöåññîâ // Äîïîâ³ä³ ÍÀÍ Óêðà¿íè. 1999. ¹11. Ñ. 100 – 103. Ïîñòóïèëà â ðåäêîëëåãèþ 03.09.2000 Ëèçãèí Âàëåðèé Àíàòîëüåâè÷, íà÷àëüíèê îòäåëà ÀÑÓ ÀÎ “ Ìåðêó- ðèé ” . Íàó÷íûå èíòåðåñû: òåîðèÿ âåðîÿòíîñòåé è åå ïðèëîæåíèÿ, òåîðèÿ íåîäíîðîäíûõ ñòðóêòóð, ïðîãðàììèðîâàíèå. Àäðåñ: Ðîñ- ñèÿ, 357100, Êàðà÷àåâî-×åðêåññêàÿ ðåñïóáëèêà, ã. ×åðêåññê, óë. Êàâêàçêàÿ, 126, òåë.: (87822)511-51. ÓÄÊ 519.872 Â.Ï. ÂÎÐÎÁÜÅÂÀ, Ñ.À. ÌÀÐÒÛÍÎÂ, Â.À. ÐÓÄÀÊÎÂ, Ì.À. ÕÀÆÌÓÐÀÄΠÐÀÑ×ÅÒ ÌÀÃÍÈÒÍÎÉ ÑÈÑÒÅÌÛ ÒÎÊÀÌÀÊÀ Ñ ÂÀÊÓÓÌÍÛÌÈ ÌÀÃÍÈÒÍÛÌÈ ÏÎÂÅÐÕÍÎÑÒßÌÈ ÑÐÅÄÑÒÂÀÌÈ ÑÀÏÐ Îïèñûâàåòñÿ êîíöåïöèÿ ìàãíèòíîé ñèñòåìû òîêàìàêà ñ âà- êóóìíûìè ìàãíèòíûìè ïîâåðõíîñòÿìè, ïîëó÷åííûìè òîêîâûìè êîíòóðàìè, íàêëîíåííûìè íà íåáîëüøîé óãîë ê ãëàâíîé îñè òîðà. Äàííàÿ êîíöåïöèÿ ÿâëÿåòñÿ ðåçóëüòàòîì îïòèìèçàöèîííûõ ðàñ÷åòîâ, ñâÿçàííûõ ñ ïðîáëåìàìè ñîçäàíèÿ ÑÀÏÐ ìàãíèòíûõ ëîâóøåê ñòåëëàðàòîðíîãî òèïà. Ïîëó÷åíà âàêóóìíàÿ ìàãíèòíàÿ êîíôèãóðàöèÿ ñòåëëàðàòîðíîãî òèïà ñ óãëàìè ïðåîáðàçîâàíèÿ 0,1. Òàêàÿ êîíôèãóðàöèÿ îáëåã÷àåò ñòàðò îìè÷åñêîãî ðàçðÿäà çà ñ÷åò óìåíüøåíèÿ òîêîâûõ ïîòåðü íà äèàôðàãìó è ôèêñàöèè îáëà- ñòè îáðàçîâàíèÿ ïëàçìåííîãî øíóðà. Èçó÷åíà âîçìîæíîñòü êîí- ñòðóêòîðñêî-òåõíîëîãè÷åñêîãî èçãîòîâëåíèÿ ñèñòåìû. Ñóùåñòâîâàíèå ìàãíèòíûõ êîíôèãóðàöèé ñòåëëàðàòîðíîãî òèïà â òîðîèäàëüíîé ñèñòåìå ñ êðóãîâûìè êàòóøêàìè, ïîâåðíóòûìè íà îäè- íàêîâûé óãîë n âîêðóã áîëüøîãî ðàäèóñà òîðà R, ïîêàçàíî â ðàáîòå [1] (ðèñ 1). wx}hUeܽn6q[m(H6lm3Ga06cJ͹ ڲZa W9^DArdaE"#zm{Q=~.!f}X de>xul ƺ*> A=Y%[ P1y>>uGj%. `?h<7E] G{ N%_7gggAxf53hh؋?odK^8󩕜yp#LF?5VWsNϽV[->XCKG_=p RWPA|$;-&uqEp Lf-p3 -e{ja/ZIouN9PAjDA; ư^| 6⣿9x <0w'? {*܏cy*"{Xr^Ƌg?~yU|gϿ~ŶUG{x~vz[o]g?beOsluo5٨냿yv %_:# o޻?9⋔iĂ\m<}Geo][޻},lۛ~T[٨t% kɗgMrz=/8<7:ߤ{)līd} ET+Uws*"_vxT_S"\'msoqۼ۔^.~).d~oAw65ŧlS`@nDmOkFXX˼mJAWuۼy-Q?b<"G,yT'k͋}0ڌFS'?фSg?dϑ_$֡JKu_+UOvGoWKyQYAڵr2Yz?9DI䊻OGT|ꓮoxƔʕXӲT//ӛx$ OǴ=[}_:j:*?h'9ו<:yLt,<uR3EU|EQVo+AAWUAײYzLVZuul,?!_ovmi*>mv9/iФSԸlPe,݈%zAj,)O FyvrݒIN}g'oQ9%Ot,{M}}Y꿮Pš4NUW`O|ś;ȓVv=DED:p%C|g'KhL~*S?goMiza$/{twXMo]&pfA7*{Zy(o&>_~+/PG|amAVAV x1DG {JC8t'ic)_> Z-B]|]PM%~E'f(y' xmo]ʂJ`UTf{*頮/*3AU_<*t|Uh+N9_ wSCWj:دF>@;' >Fҁ_ҟbSŪ9U4{u-ulrbϐ'mf5jv,n6~JAGXtŋdWZ}Q2R?=>WuFPpӟǞ]ă|ʃ‹avVgٞw|g_Bŋd'|C{2!>̷F{2{d$s'ҫ&'8zr␾sɓݴ;){7eO,|֡^-ِҲΐ/TLת9=.~ŋ?xy1ʜEeEeCc"Зl/dU BoF?a||U&o){"hyo'L¼5l꺿[&/Ur`{? 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Ñîçäàíèå êðóòûõ òîðîè- äàëüíûõ ñèñòåì, â êîòîðûõ ïëàçìà èìååò âûòÿíóòîñòü âäîëü ãëàâíîé îñè ( Ý = â/à, â - áîëüøàÿ îñü ýëëèïñà, à- ìàëàÿ), ñâÿçàíî ñî ñòðåìëå- íèåì îáåñïå÷èòü óñòîé÷è- âîñòü ïëàçìû â òîêàìàêå ïðè äîñòàòî÷íî áîëüøèõ ïëàçìåí- íûõ òîêàõ [2]. Èíòåðåñíî èçó÷èòü âîçìîæíîñòü ïîëó- ÷åíèÿ âàêóóìíîé ìàãíèòíîé êîíôèãóðàöèè â êðóòîì òîêàìàêå ñ D -îáðàçíûìè êàòóøêàìè ÎÒÏ. Ïîâåðõíîñòü êàòóøåê ëåãêî îïèñàòü âðàùåíèåì âîêðóã îñè Z ÷àñòè ýëëèïñà, îãðàíè÷åííîãî èçíóòðè ïîâåðõíîñòüþ öèëèíäðà. Ëèíèè ïåðå- ñå÷åíèÿ ïîâåðõíîñòè ñ íàêëîíåííûìè ïëîñêîñòÿìè îïðåäåëÿþò ôîðìó è ïîëîæåíèå òîêîâûõ êîíòóðîâ, ñîçäàþùèõ âàêóóìíóþ ìàãíèòíóþ êîíôèãóðàöèþ. Ðàñ÷åòû ïîêàçàëè, ÷òî ñèñòåìà çàäàííûõ òàêèì îáðàçîì òîêîâûõ êîíòóðîâ ñîçäàåò ìàãíèòíûå êîíôèãóðàöèè ñòåëëàðàòîðíîãî òèïà â øèðîêîé îáëàñòè ïàðàìåòðîâ òîðîèäàëüíûõ ñèñòåì (ðèñ. 2). Èçó÷åíû òîðîèäàëüíûå ñèñòåìû ñ ÷èñëîì íàêëîíåííûõ êàòóøåê ( N ) â äèàïàçîíå 2-24, àñïåêòîâûì îòíîøåíèåì À ê = 1  10, ýëëèïòè÷íîñòüþ Ý ê = 1  3, ñ óãëàìè íàêëîíà òîêîâûõ êîíòóðîâ n 1  5  16 î (è áîëåå). Âî âñåõ ðàññìîòðåííûõ ñëó÷àÿõ íàéäåíû çàìêíóòûå ìàãíèòíûå ïîâåðõíîñòè ñ óãëàìè c â èíòåðâàëå îò íóëÿ äî íåñêîëüêèõ äåñÿòêîâ äîëåé åäèíèöû. Ãëàâíàÿ ïðîáëåìà ñâÿçàíà ñ ñèììåòðèçàöèåé ñå÷åíèé øíóðà îòíîñè- òåëüíî ÎÒÏ â öåëÿõ óìåíüøåíèÿ ãîôðèðîâêè ïîëÿ |  | / î íà âíåøíåì îòâîäå òîðà.  îñíîâíîì ýòî äîñòèãàëîñü ðåãóëèðîâêîé ôîðìû êîëåö è ðàñïðåäåëåíèÿ   ð =¦( R ). v Z I в В 0 R в 1 2 4 3 4 4 I к I в B 0  r в Ðèñ. 1. 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Êàê è ÝÖÐ-ïðåäèîíèçàöèÿ, Â×-ïðåäèîíèçàöèÿ ìîæåò óëó÷øèòü óñëîâèÿ äëÿ ñòàðòà îìè÷åñêîãî ðàçðÿäà, óìåíüøèòü ðàñõîä ìàãíèòíîãî ïîòîêà èíäóêòîðà. Â×-ïðåäèîíèçàöèÿ âîçìîæíà â øèðîêîì äèàïàçîíå èçìåíåíèÿ òîðîèäàëüíîãî ìàãíèòíîãî ïîëÿ. Ïîñòóïèëà â ðåäêîëëåãèþ12.05.2000 Ñïèñîê ëèòåðàòóðû: 1. Ãåîðãèåâñêèé À.Â., Ìàðòûíîâ Ñ.À., Ðóäàêîâ Â.À., Ñåðãååâ Þ.Ô., Õîäÿ÷èõ À.Â. Ìàãíèòíàÿ êîíôèãóðàöèÿ êîëüöåâîé ñòåëëàðàòîðíîé ñèñòåìû // ÂÀÍÒ. Ñåð. Òåðìîÿäåðíûé ñèíòåç, 1989. Âûï.4. Ñ. 28-35. 2. Áû- êîâ Â.Å., Âîëêîâ Å.Ä., Âîðîáüåâà Â.Ï., Ãåîðãèåâñêèé À.Â. è äð. Êîìïàêòíûå êðóãîâûå ñòàëëàðàòîðíûå ìàãíèòíûå ñèñòåìû //  ñá.: Òðóäû 8-é ìåæäóíà- ðîäíîé ðàáî÷åé ãðóïïû ïî ñòåëëàðàòîðàì (ìàé 1991ã., Õàðüêîâ), -Vienna: IAEÀ.1991. Âîðîáüåâà Âåðà Ïàâëîâíà, èíæåíåð-ïðîãðàììèñò 1-é êàòåãîðèè Õàðüêîâñêîãî Ôèçèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðå- ñû: ìàòåìàòè÷åñêîå ìîäåëèðîâàíèå ôèçè÷åñêèõ ïðîöåññîâ, ïðî- ãðàììèðîâàíèå. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêàäåìè÷åñ- êàÿ, 1, òåë. 37-35-26. Ìàðòûíîâ Ñåðãåé Àëåêñååâè÷, âåäóùèé èíæåíåð-òåõíîëîã Õàðü- êîâñêîãî Ôèçèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðåñû: àâòîìàòèçèðîâàííîå ïðîåêòèðîâàíèå ìàãíèòíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêàäåìè÷åñêàÿ, 1, òåë. 35-33-35. Ðóäàêîâ Âàñèëèé Àíäðååâè÷, êàíä. òåõí. íàóê, çàâ. ëàáîðàòîðèåé Õàðüêîâñêîãî Ôèçèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðå- ñû: ðàñ÷åòû ìàãíèòíîé êîíôèãóðàöèè ñòåëëàðàòîðíûõ ñèñòåì. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêàäåìè÷åñêàÿ,1, òåë. 35-69- 92. Õàæìóðàäîâ Ìàíàï Àõìàäîâè÷, ä-ð òåõí. íàóê, ïðîôåññîð, íà- ÷àëüíèê îòäåëà Õàðüêîâñêîãî Ôèçèêî-òåõíè÷åñêîãî èíñòèòóòà. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêîå ìîäåëèðîâàíèå ôèçè÷åñêèõ ïðîöåññîâ è ñèñòåì, àâòîìàòèçàöèÿ ïðîåêòèðîâàíèÿ, ïðîãðàììè- ðîâàíèå. Àäðåñ: Óêðàèíà, 61108, Õàðüêîâ, óë. Àêàäåìè÷åñêàÿ, 1, òåë. 35-07-95. 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Ëîãè÷åñêàÿ ñòðóêòóðà MISC ñîñòîèò èç äâóõ ÷àñòåé: îñíîâíàÿ (èëè RISC) ÷àñòü è óïðàâëÿþùàÿ ïàìÿòü (ìèêðîïðîãðàììíîå óïðàâëåíèå). Îñíîâíàÿ ÷àñòü Host — îäíîóðîâíåâûé RISC ñ ãëîáàëüíûì ìèêðîïðîã- ðàììèðîâàíèåì çàäà÷è, ãäå âûïîëíÿåòñÿ 40-50 ïðîñòûõ îäíîòàêòíûõ êîìàíä. Åñëè æå íåîáõîäèìî âûïîëíèòü êîìàíäó, íå ïðèíàäëåæàùóþ ê ÷èñëó ïðîñòûõ, òî èñïîëüçóåòñÿ ÏÇÓ ìèêðîïðîãðàììíîãî óïðàâëå- íèÿ. Ïðè îòñóòñòâèè áëîêà ìèêðîïðîãðàììíîãî óïðàâëåíèÿ ïðîöåññîð ðàáîòàåò êàê ÷èñòûé RISC. Ïðåèìóùåñòâî òàêîãî ðàçäåëåíèÿ î÷åâèäíî. Áèáëèîòåêà ñòàíäàðòíûõ ôóíêöèé (íåêîòîðûå èç íèõ CISC-ïðîöåññî- ðû âûïîëíÿþò îäíîé, õîòÿ è ñëîæíîé êîìàíäîé) äëÿ RISC-ïðîöåññîðà çàíèìàåò ìíîãî ìåñòà â ïàìÿòè. Îáðàùåíèÿ ê ïàìÿòè RISC-ïðîöåññîðà î÷åíü ÷àñòû è çàíèìàþò ìíîãî âðåìåíè, ïîýòîìó âûïîëíåíèå ñòàíäàð- òíûõ ôóíêöèé ìîæåò ïîíèçèòü áûñòðîäåéñòâèå RISC. Èìåííî ïîýòî- ìó â ïðåäëàãàåìîé ñòðóêòóðå áèáëèîòåêè ñòàíäàðòíûõ ôóíêöèé ðàñïî- ëîæåíû â ÏÇÓ ÌÓ. Ïîäîáíûé ïîäõîä ðåøàåò ãëàâíóþ ïðîáëåìó: äëÿ êîìàíä ìèêðîïðîãðàììû íå òðàòèòñÿ âðåìÿ íà âûáîðêó è äåøèôðàöèþ êîìàíäû, òàê êàê â ÏÇÓ óæå äåøèôðîâàííàÿ ïîñëåäîâàòåëüíîñòü RISC-êîìàíä, âèäèìàÿ ïðîãðàììèñòîì, êàê åäèíàÿ ÑISC-êîìàíäà. Êîìïèëÿòîð äëÿ òàêîé ñòðóêòóðû äîëæåí âûïîëíÿòü ñëåäóþùåå: 1. Ïðîãðàììà íà ÿçûêå âûñîêîãî óðîâíÿ (ßÂÓ) — èñõîäíûé êîä ïðåîáðàçóåòñÿ â îáúåêòíûé êîä. Ëþáîé êîìïèëÿòîð ñ ßÂÓ äëÿ RISC- àðõèòåêòóðû ãåíåðèðóåò ìèêðîêîä â ïðîñòûå êîìàíäû.  ÌISC-êîì- ïèëÿòîðå ïðîáëåìà ïîòåðè âðåìåíè íà ïîýòàïíîå âûïîëíåíèå ñòàíäàðò- íûõ ôóíêöèé ðåøåíà. 2. Ãëîáàëüíàÿ ìèêðîïðîãðàììà, ïîëó÷åííàÿ ïîñëå ïåðâîãî ýòàïà, ïðîñìàòðèâàåòñÿ ïî îïðåäåëåííûì ïðàâèëàì [7]. 3. Èñïîëíåíèå ìèêðîïðîãðàììû. Ïðîñòàÿ ìèêðîêîìàíäà îáðàáàòû- âàåòñÿ ïðîñòîé îäíîòàêòíîé êîìàíäîé ïðîöåññîðà èëè íåñêîëüêèìè èç áàçîâîé ñèñòåìû êîìàíä. Ñëîæíàÿ êîìàíäà – ïî ïðèíöèïó “ ñêëåèë - èñïîëíèë ” . Íèæå ïðèâåäåíà ÷àñòü êîìïèëÿòîðà, íàïèñàííîãî íà Ñè [5] è âûïîëíÿþùåãî ïåðåâîä èñõîäíîãî êîäà â ãëîáàëüíóþ ìèêðîïðîãðàì- ìó.  êà÷åñòâå ÿçûêà âûñîêîãî óðîâíÿ áûë âûáðàí Ñè. // File MISC Compiler Part4 # include # include ” cip.def ” extern char *mach, *cptr, *symtab, # ifdef OPTIMIZE optimize, ;xhuǟUw9E` s2ZՔY:%U¼lFDN2ׂ0 D.n^>x7y|?~o#b-Dj, H+be d+vO7W9Z/^tx_fAZPq令/3f;׊Ng ӽ,QZT#&3xmxeV4Q u x6uw/rofk|+5hM<{67[lHNF^eRzYXFk}Lߕr6_2<Dz2uF3~nNf530}f?F71ѯe岼1? /OLDXMj]z(qx55ۈ5Ek' [ Uma Q_:_)7Q^O{a= \^L"OuO]}bMhK7rֶv$IOyWWxaP}|] 7!?&;Pߋf#=CQz"B}І^B=2+{T_np3}63>X)&?D=CR=S?@ "Vq2\}tgc_TbM+-Ix Wo} r; Mľ5 3oz.G^VWĆAhqr͞Mr(#Ӿs-ЙWy:` ^>߂H؊L?d`lZ3'4ztM[7?(Uߢ&r%f%&7qc+=vqL/'M^iةIz'IȽMN[ZǞNYDir˧)w3;c4ίgܹ{ܙiKJ0t~}sFJq^Ҵ)e׮I%9'[MfAy'RzqWKh.pjȴtmڗv?eЎt@՚pOP5ik?ҧt3BW4tǛ}ǰ=7־8ͧ uCĕ9v-%9.3qu=յa>iXjk3aI0^ubqrq=`ʸw/DXl=nvzkZPJ9ovNӖ]lQܩ}ޜ1}mWnKC?ڝmKKKzO=/Пܼ<ﻎגbXpipq:}[ɴC[K[ZS[Z딾i__(ZuoQ2/q8sMFh7}?޸cƊKnBd2˗z] b~JUTʔ4moo^bZO~UnN!͑냹GMkwtܝFhMv#7_:U 1 ,8_3ۉ`ۛt05W#{KڡlA#9&[܎5X3'ۃ=ӅsPy<dY#YQgA=W/!q܆ ӎ:CȲtTޣʹcwЊmi+IF|/ˣb{V<~ {¯߰ {wtm%~K1})GA=/5_*pڇbgpuÙ"5_Nm) O@NYuFy2/u;KҒׅ.~E,xm)jܰ53 +<OG&2zxBWr9zd+͌uv>u6p> O`i%w_ux>܏,;1_F_hbxŤfAUKvy;0. yH(XΫ·WQdwMT+r=e֤ X Wko">tn`~3Wvvfllb,ϳ5beG쓌riѠm2 >'ɛNwe37>douE~#*rFU׎ͯصG;6Z={r>^hҏȅ}ԌE}X1? 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j҉~[[$`"QfEf-F*boWve;lc+nI'Ev`cx¥Vnf-ŶuxdW2=dށ}Aꗨ3#h՛Р0B-J#\{W Ϭ6lg)@_oQy.:pq@J ZJakB&#sR:^e>!S]s]ץ 6iwz"L{R tgMLh92|:8X ۸o?sƫvX+D!}ބQIW7ۘw ]H y+64,H~}Jb&,%/,ǽ8?Zx_u-}qq.t[Xxtf .>t:_l}}us~'5M;.Гu5ejO"]sx֞ԙ}ӓ.xαsM~ߙ`;Z5ͫNܚ1<~cO߶wfgko^QX18gوZCxЄMXm!62zE(ݑnbTrKO=߆vu(/пCnsʤ~3oܴlcE17//ljtܴtyz[Yn:s9{sZs77MG6.#sS#V~dnN#NG䦶W|[>OwwOwf]i `/C3yW,InM-~f:,ߝƘټF9]b}|6u;3&lFWEd7+r1Uq \;Ғl]rO#̚%k/@}Ukbs 6'6K˱{TDYFy'XZɗ%8E=U89h;y"B2c7'e܉y"r&V}E.z#ߎwæ_ވ/˸U۰_׽[kG%֙)tP9IC];8*b;8e$Ys&rϛccExng%03 k>B5+֧9i?xHV:egR)2cn>S~oױ_1Qר3m WDgVތ-P[m%Yѹq@\?-8Vbp-чNptcqkHb{yX~ ΡGuU8yG2Od#ϓ1{bO:[>dA|X<砻|&y7~+v+]c.qP'GnD|֣;y>鏕`^n,=}3{+N'ɧè75=qEAQU=[ `S 芽YtGlE[y/(_I3kpyx7K]D|\slAgSG>?#k\k D7Rg {M*غнikGe4} 11^.~*v`ڎnKܕLd'(N!GqZ/]܊[<"5#~ߥp]Rˌ/yX>@V1+EnS/cvg僽 Gg̫bv1;Emq뭿-OY664woȿTq5{-g%n9|U1Gɩ!.q8N^Z~vh8wR<x!8抬>_p"V9U(cӑ/'|ėƚt}9"]?0\>a׉ B}U|V2~O!K0E.5抹;=4pć'э;zܔ"9/WR p4ЁoY^(&3Vr;^k<Gf._Ky y`7Ve]->W_-OAkoBw55 @kz$+GZ5.έisOFMO{Ϛ_㷒؂WUiy\"ȃ%>n{Qc)uOsR^kX8%|c?5:E^s>"rZ sRo[qUiaԸ5[pZCgg*ENzFkb X7^:$iQ>k="s& \.,Y1BG+kݨ .Wbs5}ܞgD?_߹nzskL S,,91 modstk(newsp, save) int newsp; int k; k=newsp-cspo; if(k==0)return newsp; if(>=0) {if(k<7){ if(k&1){ ol( “ INX SP ” ); k—; } While(k){ ol( “ PUSH B ” ); k=k+BPW;} return newsp;} } if(save)swap(); const(k); ol( “ DAD SP ” ); ol( “ SPHL ” ); if(save)swap(); return newsp;} doublereg(){ ol( “ DAD H ” );} FILE : misc42.cpp ffadd(){ ol( “ DAD D ” );} ffsub() {ffcall( “ CCSUB## ” );} ffmult() {ffcal(CCMULT## ” );} ffdiv() {ffcall(CCDIV##);} ffmod() {ffdiv();swap();} ffor() {ffcall( “ CCOR## ” );} ffxor() {ffcall( “ CCXOR## ” );} ffand() {ffcall( “ CCAND## ” );} lneg() {ffcall( “ CCLNEG## ” );}}  xSOHQf+ݵ,(L+Ւy:RVRF^\(=DBa)Azȓ:3GTtڷ~3|oy!v4+CP=z1 $*Y5(Ssy^&ڹ`84KɊ:n; Microsoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:30  l v \d(162/r1t*> {Tx_U/!l?o @6& qm1-icTMkglǙN:bִQASM(i lHhҮϽ}{!dZ;ӗ9{;s=s{!iR+i!,>U~s kCh.k0];KOaO=qIN7Çý?ܣ\Ȓ>u۬9BRWo=2zeYvwuI0Gp4n{f~%9U}`*GЈM0KuM_g X(3f%|TH ;|Zs:z񻢮K*{C7eN:+l:[[f/_L~siso^u54wNWW`X# Z.ar3;VE0 v:rQAlkwxD}MuEz}]aY9;Pj?ݱ|+􍿭?۶/]?xg<|АŸFH+z&"ܕ&R<XUW^iJb }%@ia%d~iJzF t6]i o!kٴ`1ff ri#m_j؏5p~kE=Z;w[F)Gqu ĸaq }FuO𜙷}v  9Ͷ}>h1 _cu=BpWmYJ3}17G/* ~r~e8k"姴R(0sHg9/!. >ACC^We;iNq߼ òsLCLc`=-(mb;pK[ggD# 1>h]Cq}{>υ~{K,mzCnth{؁ DIò-Y=BsϐZ{BR^x$)"qDjUZ/q']tD ;9ڒG5sG)mпB&؃:}ѯ~WhyË-W XsdgT^Ɩ±/mm oǔaҸy|̑1fư5~_e {Y;ٿcwt# MkGHLH;}rf [,i#b<'`Wt=oJtn% 6o?CۑҾKm)Sg c^Jpf<o|}i]#=bGυ\m|ih>Yϳ  jvpsϊv|!<=Q[6ï]BEv|4F|ßY-|k[ԽGb}4ir9뜵\|r̗1OϕΡy?Bs!zv<4vȅuJK@6<`ً^k+9ᖋ^[D[ }-Ϟ;T8r^2i7 [eI[oU[#ޅBўu ~PEd ̗Nԙ;-b>V4%p~!_J#^!2Xi oG_ ;@66wu6^-%p5j-(69>^)V4zg.@կa;Ǽ7ÜW >2m 93rn.q:%w ZA}WW+}Y{PoϟZ_x8vƹΨ7=>BvKJe@{YcU6Kmp}h#|̵ًU. :O1f])z6B7ޫy8_Z~_r$_ܠpobE*}cáhBt 7u\:V @O$<] uSzS?]F:7}rx/Fy.}'oseOԉE̋ulBGuC0_Eq2^6껨l'1ce s=|zuS%KtZՏm|uw /<:vx}*2e&*µt_|*W]3g~~߮t}y'1Ec(:0q] 8xƺ%#70:to1]\cVSdb`#|^]^d_> tymwZeSc:?fнs/1lW._|ŀxIm4w [2“j4[-[&Y'L=uɉӌ4qLߓ#{xy&pJ+ #FpɶLn}I1IW 8%0_r8t?z)Qd>;ѝcKN;1/6:m*AÉK)/=NmD1KK}^Rhwc>DbK!4y^ZF*iy6j3/qﵒy"I _U흗=VM_$ ~#x9F&YH2w2F&YR橲{uЎF&$y3$ }F&qK.GI.=CI6ϥKriڜsrKO7RwҳCg< #\~aҾ=)f.\ \Jruy4v"xUs)<)EЎ5ҧ}Lf.EsqʥjlK8i_^eKM8r A~|ugtҜw3^~e<<=.t!5~W} ռNFI'ȜSZ9])F[)DR7h({Eۤ"{_{-u)|'%q>ǀ?3/sX)`/ET9rn(W`}@[#du ,>kNO7Ӵ;ungS}3/]/cxt6~1[`YЩOPgrd:.~C37_1ph[vwK;}b'h]%:;m[:B7cC_-t[eǒieXRtlB[I#^_#p`Jsf֩u z)>pvD!66:Cs.cqWesv *lucmo?+'bHW_>m h$nYs-7‘q+N_<̗1|whCg=r Aq鈸%遘݊='eF.!N9T %7?}N Ai-Uoα]]5$.εZ}otnh:0G;J38 ~,uo][tcB^}FK{Mj12uzFtը>gE9WľzϚhqbwk>JV:틔ԝ 2:c- m[|YCuh| АO{(MG^c9`b6?jEqήwv̿Hty_eGU 9]"&\*fkVV VK8sEhŋ|;}#CʥQ<Ȓɘ?R>APbv 6z!=qhJX պWK_HQE=cĦx`u/1+r o]۷ʆ_pK1i+9xH3 Կ~Ǥ)L+KQ,E H+4<,{˼ѧmkz=)sB)`c8e~62g\nKd;>#RnkAPl^+&Үֿ[Pf}qǻ-zs*]pɞ_`bbDžޣb#8:qtӌ\>Ai}{-croy=~p TmlzĎ%'>Oh%+%1 ŒɭA>0o}Hc@̛짞?4tĒ4pŚz 5?A>8%˥?Бݼy߼NIoQy%ܥth)BJv ؈7v}yځ~@\E{Eq~+/t-%z{4C@[hG7MI{ϺK@\!0?-c~J>50/ 7+XԌ0,, 92 Íà ïåðâîì ýòàïå (÷òåíèå èñõîäíîãî êîäà è ñêàíèðîâàíèå) ïðîèñõî- äèò çàïîëíåíèå òàáëèö, îïðåäåëÿþùèõ îòíîøåíèå èìåí ôîðìàòîâ ïîëüçî- âàòåëÿ è èìåí êîíñòàíò ñî çíà÷åíèÿìè ïîëåé áèò. Íà âòîðîì ýòàïå îïðåäåëÿþòñÿ ñèìâîëû äëÿ ôîðìàòîâ, ñèìâîëû äëÿ êîíñòàíò è ðàçðÿäíîñòü ñëîâà ìèêðîêîìàíäû. Ñëåäóþùàÿ ôàçà – ãåíåðàöèÿ êîäà: ïðîèçâîäèòñÿ ÷òåíèå ñèìâîëè- ÷åñêîé ïðîãðàììû, ïðèñâîåíèå ìåòîê, óñòàíîâêà àäðåñíîãî ñ÷åò÷èêà, òðàíñëÿöèÿ â äâîè÷íûé êîä, ôîðìèðîâàíèå ëèñòèíãîâ è òàáëèö ñîîò- âåòñòâèÿ.  ðåçóëüòàòå âûïîëíåíèÿ âòîðîãî ýòàïà ïîëó÷àåòñÿ ôàéë, ñîäåðæà- ùèé îòòðàíñëèðîâàííóþ ìèêðîïðîãðàììó. Ýòîò ôàéë èñïîëüçóåòñÿ çàòåì êàê èñõîäíûé äëÿ ïðîãðàììèðîâàíèÿ ÏÏÇÓ ïîñëå ñîîòâåòñòâóþ- ùåé îáðàáîòêè. 2.Ñèñòåìà êîìàíä äëÿ ÌISC-ïðîöåññîðà Ïðåäëàãàåòñÿ îðãàíèçîâàòü ñèñòåìó êîìàíä ïî ïðèíöèïó äåðåâà (ðèñóíîê).  îñíîâå äåðåâà: áàçîâàÿ ñèñòåìà êîìàíä, ñîñòîÿùàÿ èç 10- 20 êîìàíä (ïðîñòûõ – êîìàíä RISC-ïðîöåññîðà, âûïîëíÿþùèõñÿ çà îäèí òàêò). Áàçîâàÿ ñèñòåìà êîìàíä (ÁÑÊ) âìåñòå ñ ïðåôèêñàìè äëÿ âõîæäåíèÿ â áîëåå ñëîæíûå êîìàíäû îáðàçóþò áîëåå ñëîæíóþ ñèñòåìó êîìàíä [3]. ÁÑÊ + Ïðåôèêñû Áîëåå ñëîæíàÿ ÑÊ + Ïðåôèêñû . . . Ñàìàÿ ñëîæíàÿ ÑÊ Èåðàðõèÿ êîìàíä äëÿ MISC-ïðîöåññîðà Äëÿ êàæäîãî èç íàáîðîâ êîìàíä èìååòñÿ ñâîÿ ìèêðîñõåìà ÏÇÓ ìèêðîïðîãðàìì èëè ñâîÿ ñõåìà ëîãè÷åñêîãî óñòðîéñòâà. Òàêîå ïîñòðîåíèå ñèñòåìû êîìàíä ñëîæíîå äëÿ ðåàëèçàöèè, íî âåñüìà ãèáêîå è çàäà÷ó áûñòðîãî âûïîëíåíèÿ êîìàíä (áåç äîïîëíè- òåëüíîãî îáðàùåíèÿ ê ïàìÿòè) ðåøàåò: 1. Åñëè â ïðîöåññîð ñ ñèñòåìíîé øèíû êîìïüþòåðà ïðèøëà ïðî- ñòåéøàÿ êîìàíäà, òî îíà âûïîëíÿåòñÿ ïðîöåññîðîì âûáîðîì èç áàçîâîé ñèñòåìû êîìàíä. 2. Åñëè êîìàíäà, ïîñòóïèâøàÿ â host-ïðîöåññîð, ñëîæíàÿ (ò.å. íå ìîæåò áûòü ðåàëèçîâàíà êîìàíäàìè èç ÁÑÊ), òî ïðîèñõîäèò ïîäêëþ÷å- íèå òîãî ÏÇÓ (íà óðîâíå êîòîðîãî èìååòñÿ òàêàÿ êîìàíäà) ÷åðåç ëîãè÷åñêîå óñòðîéñòâî ìèêðîêîìàíä, ãäå èäåò âûáîð ñëîæíîé êîìàíäû èç ñëîæíîé ñèñòåìû êîìàíä ñ ïîìîùüþ ïðåôèêñîâ è ÁÑÊ. xmheǯw<B`m#Md,DOҲHr>M)PPa#2[Ҕ"F,?> M~9aga<뾟q̩Y 7D*g=ZL"U{E*۫Cݛneo6V>&4)5V'S^lwOg}lIhOoq?lڝ0C6ƗN{ Vs*Wd;W*&wJYEs?=Hߘ~Egl\ L<[rqFH5т:ժLu}ºe?@-S_>& e2 XV@U'WϽ<*GksyN?d"mfuֺa^H.s6~wScw@gB ߯m|`_GQ_kuI g.խPS~;[ }IԵ 01; +m6Ο6^b])N}|Sg3ҺKIiVzg߂sҳm?1{}ՎOu[6}cihDj)LysM{K˺zlzc =[*znE]KfM,қ}gM;63sgұͷuwQXQ-|hLig to:9PxQ,n-N!7򌁥˷o c6d1m7R Qvc^>Ӷ6 [gbh,/˅Ѷ)O!s6%b"O(ž쫘񲌜jh؊}lWoʷgK*3'<́zm[dΈi}lܘG٦9.1<ןn@g;ʈ9(q'&m ?M%9Նvm5{7mލIlb,%sVeô~`E^WWصho}q ?;؉C57q}9t[>QLa/FDZ"">yu ¾6m9b?kqT k㸦;Z9=2Xy o&G/3Zvb=P7TB 7Ts<-)sD|@`'NlcyǘH]۔7U|uXwBcvkϙ)`FV"-m ۩K]2ھ)&됭NKˉ*.,EFC}* e(f[&epMk=,ze~,c(8;`]ކ#ޟlo7ޗ~ _z?z͕&6"[ÿx)s3|Xd{|$62LZNRֱd\Zf;㈍z!ubrqOla ,̵Cba=T_I['PݦGM?DʕhW9f1g3yh $W۵)rGPd_VXW]2jKSnCv |f* s!Kg)փo; ОLȴGMGքS_]o=7Gqxe yux F\/a,O$>{zĸs(o %O1Olc=iXJ^;BqWkOǭ-x8og&|6#fTTp*1*}X;ȿ4˫>a/|Vs|.T@PK3;u1.&_>gu;i~7(##;`FLc~V#n~wh>W8Ll:;]`a>z]2ǃ1:9ɓ ?'f1bN^76@H/拲›lc.qc<%Ǔ3׺)n+@~9z1ꃲ(N\XG{]gOu2ӨW !#+ eAoAc܏6a ,x-ǯP9-܈4u{-$3 K)/vbVEs_%u : |P)]{OA`|pߨۡL;ɎMȌO5յݶ->xǞϝEfS~Xolms]ȸ]3z> ogGbe]_;A:yUA6hWnvtzUשLi[zߎ7򻐟߻og,gL1mv>P2Dn>ί:xĺ/V#Frq-ۥm59w_Qd7x'>kQxާSxlS7"{2#s#:27ɼsBۘ'b-1L%ji;޸z-k!1 6'(xhgɉ Oտ|_ۚل3ӓbd@ވ[x*M`[q(X ÛhK5w_Z<\W~s +D+?~&k~G[΃ (l5/v]Lkz/1DLorL}61|oB60W~mj={Uz/fLed%u< /_zZWeb&^Za;1Tj-#>[MقW]k$|'wy7z7$yOGսS (E}$sn׮ǖ&_lk!}3<|*813wquԯ=MyYjI(x8( xo<'_-wz&e$^M6}Y^72>1?GQ7 C/ 9fCcd],"fh,_rZ ?vc-j-+S7YZ,8OKPYv?.cZOV4Ib9SV}chm2򻶜}HL ݏ{{vu]~k~/ξ8]!{>h{yyc['Řq_Ouۅ1:m>Dz^@>!c3">O;eS]M޾;u|軐-A蛓c6F'SGi,{waUL?}Seк21yTqu9Pe2oLlo[ˈWho.(^{m(4[\kE'= #>XTsb9w|rqݏ}>þ+4Eu$RO\G,MwM`z|lȡ_Q<~1v,cVw9nw mO49:=F+bQFVNh]7!I9T=ƻ9s#1}oXm\EuE?GMS2ޜ᝾Y88bg)϶!j6/svNWMDlgln푌<۩ñh/O3څ+iӃtbB&x{b>gO%5o]ǹog}MUߴݹϮ9h~%{3 a;c^Y;ʩߪ=ϔߪ=5횩2~cVSϿU{DUQZoզ6,ߪͣ|Ugjq{ZVsn-9Ҕk=^\q9e ^;q1-'&>;Y'y2= 8Y8s2ys!6dҼouXuYF?HIg|Un91o|tQxIk]/A=#_lWꐔWuNj>/:eWucrG[;F>־r& s=e ^uY M܈;8Aj[?͒1۴uc6fW= 'mۆAڿn2GhzN'@q3O} ehh=ܓ=_⡏RuGwM\oP^}v1 \Sչ:\ny?n뭻+kF·1yOA>i@_y(/ QyQ>‹gmYr8.煺7-ϱy`]͑Kٺ RX,RX – Ïðîâåðêà íà áîëüøå Âûáîð òàêîãî ïîäìíîæåñòâà êîìàíä èç âñåãî ìíîæåñòâà âîçìîæíûõ îáîñíîâàí åäèíîé çàäà÷åé ïîâûøåíèÿ áûñòðîäåéñòâèÿ ïðîöåññîðà. Ñ ïîìîùüþ òðåõ îñíîâíûõ îïåðàöèé (ñëîæåíèå, âû÷èñëåíèå äîïîë- íèòåëüíîãî êîäà è ëîãè÷åñêîé îïåðàöèè È/ÈËÈ) ìîãóò áûòü âûïîë- íåíû ëþáûå äðóãèå àðèôìåòè÷åñêèå è ëîãè÷åñêèå îïåðàöèè. Îäíàêî â áîëüøèíñòâå ñëó÷àåâ íåîáõîäèìî óñëîæíÿòü ñòðóêòóðó ÀËÓ äëÿ ïîâû- øåíèÿ áûñòðîäåéñòâèÿ ÌÏ çà ñ÷åò ââåäåíèÿ íîâûõ êîìàíä: âû÷èòàíèÿ, È-ÍÅ, èñêëþ÷àþùåå ÈËÈ è äðóãèõ. Çàêëþ÷åíèå Äëÿ ñîçäàíèÿ êîìïèëÿòîðà ïîä MISC – àðõèòåêòóðó áûëè âûïîëíå- íû òàêèå èññëåäîâàíèÿ: – ðàññìîòðåíà ÎÏ ñèñòåìà âîçìîæíûõ êîìàíä äëÿ Ê1804ÂÓ4, Ê1804ÂÌ1 è íà åå îñíîâå îáîñíîâàííî âûáðàíà áàçîâàÿ ñèñòåìà ïðî- ñòåéøèõ êîìàíä äëÿ MISC – ïðîöåññîðà; – ðàññìîòðåíû âîïðîñû îðãàíèçàöèè ðàáîòû MISC – êîìïèëÿòîðà íà ýòàïàõ ñêàíèðîâàíèÿ è ãåíåðèðîâàíèÿ êîäà. xhUeǟly7@2Y6ɲ(]Y6 3V -Y$aki?sr/s>>=<PDV,=`wHs,c!QC 5y?"wO+CՁ[;M쬚)d3z3g^$m&?\ʟL3dz(m%#fY foz;9wW3尯9z$o2sJn7heHz--w̖@4wyַɛkzcf5r~s!gjՌسyhkiX3ߚ|L6nyh9V4LE"9W}|lU?nkWY~ep9]^,znavqu}@>':44zơ]R [; ]ҙ&!)3k_Ý;%L 0W݇ί@>~5Xsm'auΘ^|y5[۹S'k|):i .)C7Gɟ `[,vN=}!P;XoI?O;%K3oǦ{ \A> nm,hwZk+ {TΑ?.M2,:@\%1b]Iu3b {?<0sz&pxؙڂz=i/9k-gjJ"azj/}WpK0KCnu^u!\+œX){֜_uE]A,ЌkW4do5A!,w[}4To h~-;.G'>Wv&2pړ@W=(y'ʉk+Uv3gFm.Ya "ja'ɵ $}ۄ ~G+syd1aBWh>$|4\.{5|L^5f/[]h+_aQ;]!^&'_؁a4"[ژ~a/F{cY cї\AMQ~?mݏOxs\?o<[>9\T1Ea3t1WbU4*͡WX>kGyUaxmA?#-jWWDVH% W_*=ZOVtvFd@GPԮ_4ƅ7=j >0l}C =A6xF'g\tt_ @?x2G1lk }xCζy`K@];&z,-yh詊7y۠0+QlWkg.h>L(?Oi*/<#w3o|IYDv6l_6daUQemVW:33UM;A>׳+vu)Mb~ǐFMG8'r<;N%LmyA:=/ ]9oؕ>_ 8c6 .RxwpiI[Eex/>Am_1 16nI})@݉رcq"۪HkOYdoT{4azt.b0I6~ L| m 0q%O\s)Gn!u1v_ A6G޺h[Jfs1I]_i9 C}] YgC?ڌ ɱň\]VaԱբ*F;(=}$rf=;ΰGhmիKNPTTd@9mUV.IF N -SAw9Ll܇XkrsYndy4x]Бg,0$uy||F|76YU]-k_\.o>.)M'$ǘ ؄=#ھ|) C OiCOkBsr*?vgGUmT =' z@?6 |u~7ydzϞMߋj=r_r@4*_-=)cf^1.My\x~$ޖX_ڊݢEXtQ9L+;6y ϑb]/s ~wЈ-;rI#{!Ciܡ,x~^яpoLxӳCG%K\|:߹8yyõZQs̨!cF-FIrS9ƴr.c!{.c<ܦf\=7߃&Z;5}h7I*;{;F25ZeۊxjD>oxzUy)yC_O.9r%]fq`@aﳦT8KL^4 &)j 8or;'=ص3v-$X-8[a%"m|ORKBշ@;3w)jqR͏yRwEA<9l?+#rP+9}&C !t|N_d ۦM_)W۵F_S_[ ['۪ڕ߉ n7x{GIbx=AF;Fm+66FTe*x 5Vꃺ[.QijQ5?* ':Ϊ'6aS;_lYb/Ė~.Xz$._:!6K*"^)`|e'ç!YBPC16{CYdײ`yi?ک^{.`Mc}w:#6]?Qh̵*6+ˣp߿[y%Kk4s˶wנ84F~{I{e{a/Yex4RN}Y'Je9 YhާO-4wrMIi"]D_\W,[O)Gfw1g;3>]:^^mqj9".r%Ȑu,, 94 Ñïèñîê ëèòåðàòóðû: 1.Áåðåæíàÿ Ì.À., Ëîáîäà Â.Ã., Öóêàíîâ Â.Þ. Ê âîïðîñó ïðîåêòèðîâàíèÿ ñòðóêòóðû ïðîöåññîðà // Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. 1998. ¹2(3) .Ñ.120-124. 2. Êîìïëåêò ÁÈÑ Ê1804 â ïðîöåññîðàõ è êîíòðîëëåðàõ / Â.Ì. Ìåùåðÿêîâ, È.Å. Ëîáîâ, Ñ.Ñ. Ãëåáîâ è äð. Ì.: Ðàäèî è ñâÿçü, 1990. 256 ñ. 3. Ñèçîâ Ê.À. Ìèêðîïðîöåññîð áóäóùåãî: RISC, CISC èëè MISC?// Áèáëèîòå- êà èíôîðìàöèîííûõ òåõíîëîãèé: Ñáîðíèê ñòàòåé. Âûï.1 / Ïîä ðåä. Ã.Ð. Ãðîìîâà. Ì.: Íàóêà, 1990. Ñ.118-124. 4. Åëü÷àíèíîâ Ä.Á., Ëîáîäà Â.Ã., Öóêàíîâ Â.Þ. Ìîäåëè àðõèòåêòóðû MISC-ïðîöåññîðà// Ðàäèîýëåêòðîíèêà è èíôîð- ìàòèêà. 1999. ¹1(06). Ñ. 85-89. 5. ßçûê ïðîãðàììèðîâàíèÿ Ñè / Áðèàí Â. Êåðíèãàí, Äåííèñ Ì. Ðèò÷è. Ì.: Ôèíàíñû è ñòàòèñòèêà, 1992. 270 ñ.6. Ð. Õàíòåð. Ïðîåêòèðîâàíèå è êîíñòðóèðîâàíèå êîìïèëÿòîðîâ. Ì.: Ôèíàíñû è ñòàòèñòèêà, 1984. 232 ñ. 7. Öóêàíîâ Â.Þ. Âçàèìíàÿ àäàïòàöèÿ àïïàðàòíî- ïðîãðàììíûõ ñðåäñòâ â ïðîöåññîðå ñïåöíàçíà÷åíèÿ // Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. 2000. ¹1. Ñ.59-63. Ïîñòóïèëà â ðåäëêîëëåãèþ 02.09.2000 Ïåòðîñîâ Äàâèä Àðåãîâè÷, ñòóäåíò ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: àëãîðèòìè÷åñêîå è ïðîãðàììíîå îáåñïå÷åíèå ôóíêöèîíàëüíî- îðèåíòèðîâàííûõ ïðîöåññîðîâ. Àäðåñ: Óêðàèíà, 61137, Õàðüêîâ, óë. Ìåæëàóêà, 11/7, êâ.67. Öóêàíîâ Âèòàëèé Þðüåâè÷, àñïèðàíò ÕÒÓÐÝ. Íàó÷íûå èíòåðåñû: àëãîðèòìè÷åñêîå è ïðîãðàììíîå îáåñïå÷åíèå ôóíêöèîíàëüíî- îðèåíòèðîâàííûõ ïðîöåññîðîâ. Àäðåñ: Óêðàèíà, 61111, Õàðüêîâ, óë. 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ÕÀÍÜÊÎ CÒÐÓÊÒÓÐÍÎ-ËÎÃÈ×ÅÑÊÈÅ ÌÎÄÅËÈ ÄËß ÀÍÀËÈÇÀ È ÒÅÑÒÈÐÎÂÀÍÈß ÑÅÒÅÂÛÕ ÑÅÃÌÅÍÒΠÏðåäëàãàþòñÿ ñòðóêòóðíî-ëîãè÷åñêèå ìîäåëè êîìïîíåíòîâ êîìïüþòåðíîé ñåòè, èñïîëüçóåìûå äëÿ ðåàëèçàöèè ñèñòåìû àíà- ëèçà è òåñòèðîâàíèÿ èñïðàâíîãî ïîâåäåíèÿ è íåèñïðàâíîñòåé, äåñòðóêòèâíî âëèÿþùèõ íà òåõíè÷åñêîå ñîñòîÿíèå è âîçíèêíî- âåíèå êîëëèçèé â ñåòåâûõ ñåãìåíòàõ. 1. Ââåäåíèå Ïðè ðàçðàáîòêå è ðàçâåðòûâàíèè êîðïîðàòèâíûõ êîìïüþòåðíûõ ñåòåé ñî ñëîæíîé àðõèòåêòóðîé, à òàêæå ïðè èçìåíåíèè àðõèòåêòóðû óæå ñóùåñòâóþùèõ ñåòåé âîçíèêàåò íåîáõîäèìîñòü â ïðåäâàðèòåëüíîì òåñòèðîâàíèè ïðàâèëüíîñòè ïðèíÿòûõ òåõíè÷åñêèõ ðåøåíèé. Òàêàÿ ïðîâåðêà ïîçâîëÿåò âûÿâèòü è óñòðàíèòü îøèáêè â ïðîåêòå åù¸ äî åãî ðåàëèçàöèè, ÷òî âïîñëåäñòâèè äàåò âîçìîæíîñòü çíà÷èòåëüíî ñîêðàòèòü ìàòåðèàëüíûå è âðåìåííûå çàòðàòû, íåîáõîäèìûå äëÿ óñòðàíåíèÿ òåõ æå îøèáîê è ïðîñ÷åòîâ â óæå ðàçâåðíóòîé ñåòè. Ïîäõîä ê ðåøåíèþ çàäà÷ ñîçäàíèÿ è ìîäåðíèçàöèè ñåòåé îñîáåííî àêòóàëåí äëÿ êîðïîðà- òèâíûõ ñåòåé êðóïíûõ ïðåäïðèÿòèé, êîòîðûå, êàê ïðàâèëî, íåîäíîðîä- íû, èìåþò ñëîæíóþ àðõèòåêòóðó, â ñâÿçè ñ ÷åì èõ ìîäåðíèçàöèÿ ñîïðÿæåíà ñ áîëüøèìè òðóäíîñòÿìè. Çàäà÷à ïðåäâàðèòåëüíîé ïðîâåðêè ïðàâèëüíîñòè ïðèíÿòûõ òåõíè- ÷åñêèõ ðåøåíèé ìîæåò áûòü ðåøåíà ïóò¸ì ìîäåëèðîâàíèÿ ñïðîåêòèðî- âàííîé ñåòè ëèáî îòäåëüíûõ ýëåìåíòîâ óæå ñóùåñòâóþùåé ñ ïîìîùüþ ñïåöèàëèçèðîâàííûõ ïàêåòîâ, íàïðèìåð, NetMaker XA èëè COMNET Predictor [1]. Îäíàêî îíè âåñüìà äîðîãè, ïîýòîìó ïðèîáðåòåíèå òàêîãî ðîäà ïðîãðàìì êîìïàíèåé, äåÿòåëüíîñòü êîòîðîé íå ñâÿçàíà ñ êîìïüþ- òåðíûìè òåõíîëîãèÿìè, íå ÿâëÿåòñÿ ïðèîðèòåòíûì. Êðîìå òîãî, âîñ- ïîëüçîâàòüñÿ óñëóãàìè êîìïàíèé – ñèñòåìíûõ èíòåãðàòîðîâ ïî ðÿäó ïðè÷èí (íàïðèìåð, îòñóòñòâèå òàêîâûõ â äàííîì ðåãèîíå) òàêæå áûâàåò ïðîáëåìàòè÷íî.  ýòèõ óñëîâèÿõ àäìèíèñòðàòîðó ñåòè ïðèõîäèòñÿ îá- õîäèòüñÿ ñâîèìè ñèëàìè, ñîçäàâàÿ èíñòðóìåíòàðèé äëÿ äèàãíîñòèêè ñâîåé ñåòè ñàìîñòîÿòåëüíî, èñïîëüçóÿ òàêèå ÿçûêè ïðîãðàììèðîâàíèÿ, êàê Perl èëè C++, êîòîðûå ÷àñòî âõîäÿò â äèñòðèáóòèâíûé êîìïëåêò áîëüøèíñòâà îïåðàöèîííûõ ñèñòåì. 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NT]s'Laz6կڎ]٠}Ycȼ l3G+sk1a%*ч}{l%z>~ÍzƟ\)IhS駿,kƕw%3ÝwlW.U [u#}H,ےES~7kY8w\3\eY=QrXf~SV#K<Žj/im $f50 }љ 4ˏ}\d+UKf簑&=dUtnS2N㝍W8OʏgW_òpA.2Q%Vn|d<'凗Z\A5p%Y:;9_NoyE_Kt/FNVNIxp -8҃K|,zt.}` i?[K]υf0Wwd-?7w ?WTJ%؎+)7ճ>]4۪nTw2~kXvuOʴ oU&S9E}%d;ll^!R/g9my&O_$ωe~+gT犒 'lwG9(lβfyN'pw{5+냵śO<؏xM<?LʆDwh,=->#Gn=JN;8;cL?R$+=We%tzgյIG߄,.bݛ6ƦoUʗѷj^ tƘCpٕjH=6 6t"Uzv Nz>9?9(-#U+zi̳>e˰{;ז~oDJ-kU9fO򹥛`wI^h*on9!߹ _`4 N0n<2y8#Y?ɵske'7[mGw3#->;c_pyZ9+:Uʒ-Ϊk_tW 1ƶri_X)Eux1*6ޜ;%eF{fÁ,8.[gÁ3:R_fᮬ.h?m'>3 m3{}Ybq-5 */w쒒-Xξ6,l/6g4̾O_vL)ytȝ-3:)M+mw*F-Q3N=5iՓ}9c<:rvd֙[b+Ѥ<#vl·2Ǩʩ}ùr%-]f6Տ+,5ޡK{FNuc8_6cLog%фi*W_/6^erY IL$V"P?<}~'~eΥ.{VNz/>l?~LEg??oDgMg}V?zs,,s96 ñïåöèàëèçèðîâàííûõ ñðåäñòâ, îðèåíòèðîâàííûõ íà îïèñàíèå òàêîãî ðîäà îáúåêòîâ è ïðîöåññîâ. Õîðîøåé ñðåäîé äëÿ ñîçäàíèÿ òàêèõ ìîäå- ëåé ÿâëÿþòñÿ HDL-ÿçûêè [2]. Èçíà÷àëüíî îðèåíòèðîâàííûå íà îïèñà- íèå è ìîäåëèðîâàíèå ïàðàëëåëüíûõ ïðîöåññîâ, ïðîèñõîäÿùèõ â ýëåêò- ðîííîé àïïàðàòóðå, îíè õîðîøî ïîäõîäÿò äëÿ ìîäåëèðîâàíèÿ ïðîöåñ- ñîâ, ïðîèñõîäÿùèõ â êîìïüþòåðíûõ ñåòÿõ.  ïîñëåäíåå âðåìÿ ïîÿâè- ëîñü ìíîæåñòâî êîìïèëÿòîðîâ VHDL, êàê ñâîáîäíî ðàñïðîñòðàíÿåìûõ (íàïðèìåð, ïðîåêò FreeHDL äëÿ ñðåäû Unix), òàê è êîììåð÷åñêèõ (Active-HDL îò Aldec Inc., VHDL Studio îò Green Mountain Computing Systems, Inc.), ïîýòîìó âîïðîñ âûáîðà êîíêðåòíîãî ïðîäóêòà ÿâëÿåòñÿ äåëîì âêóñà ïîëüçîâàòåëÿ. Àêòóàëüíîé ïðåäñòàâëÿåòñÿ ðàçðàáîòêà ñèñòåìû ìîäåëèðîâàíèÿ ñåã- ìåíòîâ êîìïüþòåðíîé ñåòè íà îñíîâå èñïîëüçîâàíèÿ ñòðóêòóðíî-ëîãè- ÷åñêèõ ìîäåëåé, ó÷èòûâàþùèõ òîïîëîãèþ è ôóíêöèîíàëüíûå îñîáåí- íîñòè êîìïîíåíòîâ êîìïüþòåðíîé ñåòè, êîòîðûå ïðåäñòàâëåíû íà ÿçûêå îïèñàíèÿ àïïàðàòóðû âûñîêîãî óðîâíÿ, â öåëÿõ óìåíüøåíèÿ âðåìåííûõ è ìàòåðèàëüíûõ çàòðàò àíàëèçà è òåñòèðîâàíèÿ êîðïîðàòèâ- íîé ñåòè è äèàãíîñòèðîâàíèÿ íåèñïðàâíîñòåé, ïðèâîäÿùèõ ê îòêàçàì èëè âîçíèêíîâåíèþ êîëëèçèé. Äëÿ äîñòèæåíèÿ ïîñòàâëåííûõ öåëåé ðåøàþòñÿ îñíîâíûå çàäà÷è: – ðàçðàáîòêà îáùåé êîíöåïöèè ìîäåëè êîìïüþòåðíîé ñèñòåìû è ñåòè â âèäå òðèàäû , ïîçâîëÿþùåé ðàñïðîñòðàíèòü ìåòîäû àíàëèçà è òåñòèðîâàíèÿ âû÷èñëèòåëüíûõ ñèñòåì [3,4] íà êîìïüþòåðíûå ñåòè ñ ó÷åòîì îñîáåííîñòåé ïîñëåäíèõ, ñâÿçàííûõ ñ ðàññðåäîòî÷åíèåì â ïðî- ñòðàíñòâå àïïàðàòíîãî, ïðîãðàììíîãî, èíôîðìàöèîííîãî îáåñïå÷åíèé; – ñîçäàíèå ñòðóêòóðíî-ëîãè÷åñêèõ ìîäåëåé ðàçëè÷íûõ òîïîëîãèé è òåõíîëîãèé èñïîëíåíèÿ ëîêàëüíûõ âû÷èñëèòåëüíûõ ñåòåé (ËÂÑ) íà îñíîâå òåîðèè ãðàôîâ, êóáè÷åñêîãî èñ÷èñëåíèÿ [2], îðèåíòèðîâàííûõ íà ñóùåñòâóþùèå ñèñòåìû ìîäåëèðîâàíèÿ è ïîçâîëÿþùèõ óìåíüøèòü âðåìÿ îïðåäåëåíèÿ êîëëèçèé è íåèñïðàâíîñòåé; – ñîçäàíèå àñèíõðîííûõ ìîäåëåé êîìïîíåíòîâ ËÂÑ â öåëÿõ ðåàëè- çàöèè ìåòîäîâ ñèíõðîííîãî è àñèíõðîííîãî ìîäåëèðîâàíèÿ [2] âëèÿ- íèÿ íåèñïðàâíîñòåé íà ôóíêöèîíèðîâàíèå ñåòè è âûÿâëåíèÿ äåñòðóê- òèâíûõ ïðîöåññîâ, âëèÿþùèõ íà óòèëèçàöèþ êàíàëîâ; – ðàçðàáîòêà ôóíêöèîíàëüíûõ è ôèçè÷åñêèõ ìîäåëåé íåèñïðàâíîñòåé êàíàëüíîãî è ôèçè÷åñêîãî óðîâíåé â ôîðìå <äåôåêò – äèàãíîñòè÷åñêèå ïðèçíàêè>, ïîçâîëÿþùèõ ïðîåêòèðîâàòü òàáëèöû íåèñïðàâíîñòåé â öåëÿõ äèàãíîñòèðîâàíèÿ òåõíè÷åñêîãî ñîñòîÿíèÿ ñåòè, óñòàíîâëåíèÿ ôàêòà íàëè- ÷èÿ êîëëèçèé è ìåñòà âîçíèêíîâåíèÿ íåèñïðàâíîñòè [5-9]; – ðàçðàáîòêà ìîäåëè ñåãìåíòà âû÷èñëèòåëüíîé ñåòè ñ èñïîëüçîâàíè- åì àïïàðàòà ñåòåé Ïåòðè, êîòîðàÿ ïîçâîëÿåò àíàëèçèðîâàòü òåõíè÷åñêîå ñîñòîÿíèå ñåòè è îïðåäåëÿòü äåñòðóêòèâíûå ïðîöåññû, ñâÿçàííûå ñ íàëè÷èåì êîëëèçèé èëè ôèçè÷åñêèõ äåôåêòîâ [10]; – ñîçäàíèå ìîäåëè îïèñàíèÿ íåèñïðàâíîñòåé â âèäå òàáëèöû, ãäå çàäàíû ôóíêöèîíàëüíûå è ôèçè÷åñêèå äåôåêòû, âîçíèêàþùèå â ñåòè íà êàíàëüíîì è ôèçè÷åñêîì óðîâíÿõ, â öåëÿõ ðåàëèçàöèè áåçóñëîâíîãî {"xhuǟݏmKA3ܜ4#iS&:(ibD1l+JPkܙDFVj."lh:E sOy|yD"2+R{D+_> 4D^T}3o/҄|a<傔/O4ؒ?_M$i<#;hvBFGz翼$#`^,9W%LUonW&jCzi cs65aW(Ǟ<:~f>hvbnG?]#ssغ5{R2͚q柉]Iy.}`|!E3ZA)zvu׊K`*N|_jA O_)I{/~뗓 _bGԊM5vΛ)]r:D^biya)F;B`@)h| \OVԳ}@7uKh>W,ѯslėwz0o$Sjhύ&f\eg9%ˈU)P#o( ]o9EVI#awnZvCuS|Nw59t]g]@DxW9oK&$ӗKE/W~q8&;M._1]ƳLs9ib_Y3Ox6s)/[,`8&W|yb))6ѬN\yNf\Qn݀w p7n \ vn݀w _nvMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:30  "J (16~2/y(1{x ŕ{pPe (*^ !Btb8\̪tKI APT?L$DL$1OѰ7*|: uTT}uf~_f e_=Twթ9uNUwuOQ3D=ZOE A(ڞAn -h/-??0^y"?8L  r _oXm`UFGt= .};ztt_OZAwQUTRNW껕_l犃^:#%ʉqTr֕)WÙ͵ݻRwL6K-5TW`J+$BYsN r;EyJY~;m)ntgeA)>%˟zXtsx(ΓCY-鰭T]Pt\|JrNeCӗ]4,<5%ΌU%牆\=cEr) r׶7]&}zrtVYrmC(6]av\H>zD?5m"onsڠۜFq-l0(sPpRpR(ɖm2mwk#mI#?6S~#>mm0SC$5׊KqbCmrl!ms]mTmmb\MWq,$߷Uň̟dDl2pJm 5`CP䂵`hC(gsEÜuʫs7ޛa&xO5A ֠6aC/F!jK71)a;X-LC'Xvlev p9v''bywԳrL9%%R8MV^cso & o^DNK5F2D>~(2jld{-!gOBqyWl8F7C&ccx=ˇ <Ldou?].O978ω=S c+خ1i!e-)t7K&~ǔ7D7|+95a\IߒGi7N(/"u_vf#EnƒHqlL9F^cÈ|0Ns") J>vre_I'ĶZyś/YDa8Gha_?E+1-# #G gH͝'QfZI X0 L6\#>\~pL[6T^.N9g~Jy1n gk56|;\ݑhE u= F wM8n[7)a G }4ZJ}F&O =!GCPxZ^"p /)5qF:]->Aԭ[wHP1tz"::lmzv}M| נMˊp]1k/+T񦵉3e=DwjCY 1{"ͫ(NYУoS>fP&qq n+gr/t/ =XfR;6}98ԥɏ"Jo&<&wQa?pù8eГ-)Bd"4-WYC;t[^+G~.s{n۷*׆]1g#BWև~r0=XeE=QK2Ω QNjx>1y4bewv }Zi=Uc MJekzoļi_?r1]# gO< ? 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P̳ъ(kdp/1:ӻj bOȠBCW.]Lqt%e?y6H*VP-;=bjvu!/kbKYtύ~ßC{c&=QVIIYt|~+&<sLl}ًZx-'_C{8~-t?ŤYEk /^R^,ze=X펥fbhvmQ殝Z =|]YK}WTS"SY u{EDg?p?eߴ,,;97 ïîèñêà äåôåêòîâ íà îñíîâå àíàëèçà ôèçè÷åñêèõ ïðèçíàêîâ èõ ïðîÿâëå- íèÿ â ñåãìåíòå [11]; – ðàçðàáîòêà è ïðàêòè÷åñêîå ïðèìåíåíèå ïðîãðàììíîãî êîìïëåêñà ìîäåëèðîâàíèÿ èñïðàâíîãî ïîâåäåíèÿ è íåèñïðàâíîñòåé, ïîçâîëÿþùèõ îñóùåñòâëÿòü àñèíõðîííûé àíàëèç ñåãìåíòîâ ñåòè â öåëÿõ îïðåäåëåíèÿ êîëëèçèé è ëîêàëèçàöèè çàäàííûõ íåèñïðàâíîñòåé êîìïîíåíòîâ ñåòè. 2. Òàáëè÷íàÿ ôîðìà îïèñàíèÿ ãðàôîâ Äîñòîèíñòâî àâòîìàòíîãî ïðåäñòàâëåíèÿ ãðàôîâîé ñòðóêòóðû çàê- ëþ÷àåòñÿ â òåõíîëîãè÷íîñòè åå äàëüíåéøåé ðåàëèçàöèè íà VHDL- ÿçûêå âûñîêîãî óðîâíÿ îïèñàíèÿ àïïàðàòóðû â öåëÿõ âåðèôèêàöèè ïðîåêòîâ èëè èõ ðåàëèçàöèè â àïïàðàòóðå FPGA, CPLD. Ïîýòîìó òàáëè÷íûå ìîäåëè ïðåäñòàâëåíèÿ ãðàôîâûõ ñòðóêòóð ñåòåâûõ ñåãìåíòîâ ñëåäóåò ðàññìàòðèâàòü êàê îòâå÷àþùèå ñîâðåìåííûì òåõíîëîãèÿì ïðî- åêòèðîâàíèÿ. Ãðàô åñòü ñîâîêóïíîñòü âåðøèí, ñâÿçàííûõ äóãàìè, èíà÷å, ãðàô – ýòî ñèñòåìà áèíàðíûõ îòíîøåíèé èëè ïåðåõîäîâ, êîòîðûå ìîæíî ðàçáèòü íà ýëåìåíòàðíûå ñâÿçè ñìåæíûõ âåðøèí, îäíè èç êîòîðûõ èñòîêè (èñõîäíûå ñîñòîÿíèÿ), äðóãèå – ñòîêè (êîíå÷íûå ñîñòîÿíèÿ).  àâòîìàòíîì ïðåäñòàâëåíèè îïðåäåëåíèå ãðàôà åñòü ÷àñòíûé ñëó÷àé, çàäàâàåìûé âûðàæåíèåì M X, Y Z Z f g Z t f X t Z t Y t f X t Z t FSM      ( , , , , ); ( ) [ ( ), ( )]; ( ) [ ( ), ( )], 0 1 1 ãäå X, Y Z Z f g , , , , 0 – ïàðàìåòðû çàäàíèÿ êîíå÷íîãî àâòîìàòà: âõîäíîé àëôàâèò; ìíîæåñòâà: âûõîäíûõ, îòìå÷åííûõ ñîñòîÿíèé; íà÷àëüíîå ñî- ñòîÿíèå; ôóíêöèÿ ïåðåõîäîâ; ôóíêöèÿ âûõîäîâ ñîîòâåòñòâåííî. Ñ ó÷åòîì óñëîâèé, õàðàêòåðíûõ äëÿ çàäàíèÿ ãðàôà, õàðàêòåðèñòè÷åñ- êèå óðàâíåíèÿ êîíå÷íîãî àâòîìàòà ïðèâîäÿòñÿ ê âèäó: ( ; , , , ) { ( ) [ ( )]; ( ) } ( , , ), ( ), X; Y Z H Z f E g H t E X, H t Y t G H E X H E X, H                 0 1 çäåñü H E X , , – ìíîæåñòâà âåðøèí, äóã, èäåíòèôèêàòîðîâ äóã. Ôóíêöèÿ E çàäàåò ìàðêèðîâàííûé ñèìâîëîì X S ïåðåõîä èç âåðøèíû-èñòîêà H I ãðàôîâîé ñòðóêòóðû â âåðøèíó-ñòîê H S : H E X H S S I  ( , ) . 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O\{?aM | gH-P ,pZd.xkft͸( uf.O׫T־V+W oklf|)MAsڒ'VIB7ȣxTnX_/嘞=sw]N1up=t:9 uSK<~˄$[Os /ey@ oL9׻<l@79ɊgRͦ6n;ْ{FCJ5V0߅w$0a'[>ɹ=ou;:)M+6'gՑ,,98 Ñëåäóÿ òàêîìó îïðåäåëåíèþ, êàæäûé ñèìâîë äâóõòàêòíîãî àëôàâèòà [3]: A 2 ={Q=00,E=01,H=10,J=11,O={Q,H},I={E,J},A={Q,E}, B={H,J},S={Q,J},P={E,H},C={E,H,J},F={Q,H,J},L={Q,E,J}, V={Q,E,H},Y={Q,E,H,J}, A 1 ={0,1,X={0,1}},  (U)} åñòü ãðàô, ñîäåðæàùèé äâå âåðøèíû, ñîåäèíåííûå äóãàìè, ÷èñëî êîòîðûõ â çàâèñèìîñòè îò ñèìâîëà îïðåäåëÿåòñÿ èíòåðâàëîì çíà÷åíèé îò 1 äî 4. Îäíàêî èíòåðåñ ïðåäñòàâëÿåò íå èçîìîðôèçì äâóõòàêòíûõ ñèìâîëîâ ýëåìåíòàðíûì ãðàôàì, íî âîçìîæíîñòü ïðåîáðàçîâàíèÿ ëþ- áîé ñòðóêòóðû â êóáè÷åñêîå ïîêðûòèå ñ ïîñëåäóþùèì àíàëèçîì åå ñ ïîìîùüþ ìåòîäîâ, îðèåíòèðîâàííûõ íà îáðàáîòêó ìîäåëè àâòîìàòíîãî óðîâíÿ. Ïðîöåäóðà ïðîåêòèðîâàíèÿ êóáè÷åñêîé ôîðìû ïðåäñòàâëåíèÿ ãðàôà ïî èçâåñòíîé ñòðóêòóðå îáúåêòà ñîñòîèò èç íåñêîëüêèõ ýòàïîâ. 1. Îïðåäåëåíèå ìèíèìàëüíîãî ìíîæåñòâà ðàçðÿäîâ (àâòîìàòíûõ ïå- ðåìåííûõ) â öåëÿõ ïðèñâîåíèÿ êàæäîé èç N âåðøèí äâîè÷íîãî êîäà ïî ôîðìóëå íàõîæäåíèÿ öåëîé ÷àñòè ÷èñëà, îêðóãëåííîé â áîëüøóþ ñòîðîíó: n=]log 2 N [. 2. Äóãå ñòàâèòñÿ â ñîîòâåòñòâèå êóá êóáè÷åñêîé ôîðìû ïðåäñòàâëå- íèÿ ãðàôà (ÊÔÏÃ) C i , ïîëó÷àåìûé íà îñíîâå îïåðàöèè êîíêàòåíàöèè * 0 1 0 1 0 1 X Z Q E A G H J B T X O I Y K Z X Z íàä ñîîòâåòñòâóþùèìè ðàçðÿäàìè êîäîâ âåðøèí èñòîêà è ñòîêà: C C H H i k i pq p q p q H H p q      ( * ) , , , ( ) 1 , ãäå k – ÷èñëî äóã â ãðàôå èëè êóáîâ. 3. Èòåðàòèâíàÿ ìèíèìèçàöèÿ ( I – øàã èòåðàöèè): C C C j C C I s i I i I t I ij I tj I           1 1 1 1 1 ! ( ), , c ïîñëåäóþùèì ïðèìåíåíèåì îïåðàöèè âåêòîðíîãî ïîãëîùåíèÿ C C j C C C i t k i I t I ij I tj I ij I       ( )( , , ) 1 ê èñõîäíûì êóáàì ïîêðûòèÿ, â êîòîðûõ êàæäûé âåêòîð ìîæåò ó÷à- ñòâîâàòü áîëåå îäíîãî ðàçà. Äëÿ ïðîèçâîëüíîé ñòðóêòóðû ïîñòðîåíèå ÊÔÏà íà÷èíàåòñÿ ñ îïðå- äåëåíèÿ êîëè÷åñòâà ðàçðÿäîâ n äëÿ êîäèðîâàíèÿ N âåðøèí, óäîâëåòâî- ðÿþùåãî íåðàâåíñòâó N  2 n . Çàòåì âûïîëíÿåòñÿ èòåðàòèâíàÿ ïðîöåäóðà îïðåäåëåíèÿ âåðøèíû H i ñ ìàêñèìàëüíîé ñòåïåíüþ ïîëóèñõîäà S I (H i ) (ïîëóçàõîäà S Î (H i )) åùå íå îòìå÷åííûõ ñòîêîâ (èñòîêîâ). Ïîñëåäíèå êîäèðóþòñÿ â ïîðÿäêå âîçðàñòàíèÿ äâîè÷íûõ ÷èñåë ïîäìíîæåñòâàìè êîäîâ, êðàòíûõ ñòåïåíè äâîéêè. Òàêèìè ÿâëÿþòñÿ: (0,1); (00,01,10,11); (000, 001, 010 ,..., 111). Ïðè ðàâåíñòâå ïîëóñòåïåíåé ïðîñ÷èòûâàþòñÿ $x{lSu]7{VP$ Pʼn>Pщ&HF4>0QTp∊@$0!('k{?nK4m~w{nU+""g lӽd!r$~GX\ěߝě~R΍g-Xs쁲&4U=+~ې[9#H (]͡Ts Js_)iЍ+GM6ՉFE5}RM]ZGz2ꤶ-)ּyyDќdv1s<_g%[ %y Y H&o-Wbiu+s.dzyOl%*^9^y&·{Q=t|A*B vΓS͓c;7ٳ,E:zMrUG| U̐U2ȉu\f8gB셲/fP:gM<uN:5)>ky fD),~3Uͺ] <5Wz\oW.jsXM\|ڋ<n9D3)֑u-MNWY1*97Vk_*ì᎚}m^?σ's~|*uE56 y>@!^Vb^Yj DVѹXytZbmVэ ~7#|ձ>ze7ryl]|gKɤvLg"0omxg0!hS\xy0>B?\hlTP>FqN/3NgY9G\}g9Ԯy߬*OW>Z̷3ߕ7]֨f^U5bކ/oT59mmw[L}N>pZ:x;;cٳc솓UcOmtg=f+tטkӿtHw ݁tHww/݁tHw ݁c~YMicrosoft Office Document Image Writer 11.03.1897.00 2006:08:04 15:40:30  5 ,55(16K2(L/515DL{xgf~Abhi"QT E숉J FJTP#Hib)gwX{+fwʷsh=1=kU6&Иcyu1WT&8;7鵌y}l$]f1k79Bg WGK ZUϹ,?/1?`\XNn$[͹i j9 })dKش58dGFע%بfy92Nǀ|[i&S+~r.q9L6S1N㣴:c~L:dh;xcȪuLlۋeL}w^ܻY_jZuTZݡfs{5Lf,34=C#H'ίb u@Qs~ϠzͭP6 o߶{ g>4aQzCYJ#זǨ}ɗ?9ĠǿVOϋQYGK1>dzBXJJeۦys^Gɒs&Ķb}l~H?1Ħƃ5}V]E:60(ܦ6bS(=:W|xA(tұ9MCŦRŦR_cSJfecs7#pta'=|lГ|9fYnfḑfYDrR~&3UgSrDkSkeD+c~OŦt#9Dquʄ@uoW|ՓU: e%:W\;-hڗ\r{SaUb###'%SmPtPdmM"/_lފȬ2Z|&. 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Ïðîöåäóðà íå ãàðàíòèðóåò ïîñòðîåíèÿ îïòèìàëüíîãî ïîêðûòèÿ, êîòîðîå ìîæåò áûòü ïîëó÷åíî ñ ïîìîùüþ ýâðèñòè÷åñêèõ ïðèåìîâ. Èëëþñòðàöèåé ïðîöåäóðû ïðîåêòèðîâàíèÿ ÊÔÏà ñëóæèò ïîñòðîå- íèå ïîêðûòèÿ äëÿ ãðàôà òîïîëîãèè "çâåçäà", â êîòîðîé âîñåìü ðàáî÷èõ ñòàíöèé ñîåäèíåíû ìåæäó ñîáîé ïîñðåäñòâîì êîììóòàòîðà (ðèñ.1). HUB 0000 0001 0010 0011 0100 0101 0110 0111 1000 W0 W1 W2 W3 W4 W5 W6 W7 Ðèñ. 1. Ãðàô òîïîëîãèè ArcNet Äëÿ òàêîé ñòðóêòóðû âûïîëíÿåòñÿ ïðîèçâîëüíîå êîäèðîâàíèå âñåõ âåðøèí, ñîîòâåòñòâóþùèõ ðàáî÷èì ñòàíöèÿì, ïðè óñëîâèè, ÷òî êîä êîììóòàòîðà äîëæåí ñîîòâåòñòâîâàòü ñòàðøåìó â äåñÿòè÷íîì ýêâèâà- ëåíòå ÷èñëó. Ïîëó÷åííûå ïàðû äâîè÷íûõ âåêòîðîâ, ñîîòâåòñòâóþùèå âñåì äóãàì ãðàôà, îïðåäåëåííûì ïîäìíîæåñòâàìè { , } W HUB HUB W i i   , à òàêæå ñêîíêàòåíèðîâàííûå äâóõòàêòíûå âåê- òîðû èìåþò ñëåäóþùèé âèä: W HUB EQQQ EQQH EQHQ EQHH EHQQ EHQH EHHQ EHHH i   0000 1000 0001 1000 0010 1000 0011 1000 0100 1000 0101 1000 0110 1000 0111 1000 ; W HUB HQQQ HQQE HQEQ HQEE HEQQ HEQE HEEQ HEEE i   1000 0000 1000 0001 1000 0010 1000 0011 1000 0100 1000 0101 1000 0110 1000 0111 . 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Âðåìåííûå ìîäåëè êîìïîíåíòîâ ËÂÑ Áóäåì ðàññìàòðèâàòü ìîäåëü ËÂÑ êàê ñîâîêóïíîñòü ðàáî÷èõ ñòàí- öèé, ñîåäèíåííûõ ìåæäó ñîáîé ñòðóêòóðèðîâàííîé êàáåëüíîé ñèñòå- ìîé. Òàêæå áóäåì ñ÷èòàòü, ÷òî êàæäàÿ ñòàíöèÿ ïî îòíîøåíèþ ê äðóãèì â êîíêðåòíûé ìîìåíò âðåìåíè ìîæåò íàõîäèòüñÿ â ðåæèìå îæèäàíèÿ, ïðèåìà èëè ïåðåäà÷è èíôîðìàöèè. Êàæäûé êîìïîíåíò ñåòè èìååò íîìèíàëüíóþ çàäåðæêó ðàñïðîñòðàíåíèÿ ñèãíàëîâ èëè ïàêåòîâ. Êîëëèçèÿ åñòü ñîñòÿçàíèÿ äâóõ èëè áîëåå ñòàíöèé, ïðèâîäÿùèå ê èñêàæåíèþ ïðè ïðèåìå èíôîðìàöèîííûõ ïàêåòîâ. Ñëåäîâàòåëüíî, àíà- ëèçèðîâàòü ñåòü íà ïðåäìåò íàëè÷èÿ êîëëèçèé ìîæíî ìåòîäàìè ñèíõ- ðîííîãî è àñèíõðîííîãî ìîäåëèðîâàíèÿ öèôðîâûõ ñèñòåì. Ñóòü ýòèõ ìåòîäîâ çàêëþ÷àåòñÿ â êâàíòîâàíèè âðåìåííîãî êîíòèíóóìà ìîäåëü- íûìè çàäåðæêàìè ïåðåõîäíûõ ïðîöåññîâ è ïðîõîæäåíèÿ ñèãíàëîâ ïî êîìïîíåíòàì ñåòè. Ìîäåëü ñåãìåíòà, ó÷èòûâàþùàÿ ñèíõðîííî-àñèíõ- ðîííûé õàðàêòåð ñîñòÿçàíèé, ïðåäñòàâëåíà êîìïîíåíòàìè        , , , , ãäå    [ , ] t i t i 1 – èíòåðâàë âðåìåíè ìåæäó ïîäà÷åé î÷åðåäíîãî íàáîðà (ïàêåòà) ÿâëÿåòñÿ ñòàíäàðòíûì àòðèáóòîì ïðîòîêîëà ñåòè;     [ min , max ] – èíòåðâàë íîìèíàëüíûõ çàäåðæåê êîìïîíåíòîâ öèôðîâîé ñèñòåìû (ñåòè);     [ min , max ] – èíòåðâàë (íåîïðåäåëåííîñòè) ðàçáðîñà íà÷àëà ïåðåäà÷è ñèãíàëîâ, åäèíûé äëÿ âñåõ ñòàíöèé, êîòîðûé ÿâëÿåòñÿ ôóíê- öèåé ðàçëè÷íûõ ïóòåé ïðîõîæäåíèÿ ñèãíàëîâ îò ïåðåäàò÷èêîâ äî ïðèåìíèêà ïî êàáåëþ;    { , , , } 0 1 X – àëôàâèò îïèñàíèÿ ñèãíàëîâ â ñåòåâîì ñåãìåíòå. Äëÿ ñîçäàíèÿ ïðîãðàììíûõ ïðèëîæåíèé ìîäåëèðîâàíèÿ ñîñòÿçàíèé èëè êîëëèçèé òðóäíî îïåðèðîâàòü âðåìåíåì, íå èìåÿ íàïåðåä çàäàííî- ãî äëÿ êàæäîé ñèñòåìû èëè ñåòè ìàñøòàáà. Ïîýòîìó ïðè ñîçäàíèè ìîäåëè ðåàëüíîé êîðïîðàòèâíîé êîìïüþòåðíîé ñåòè è åå êîìïîíåíòîâ èñïîëüçóåòñÿ ïðîöåäóðà íàõîæäåíèÿ íàèáîëüøåãî îáùåãî äåëèòåëÿ äëÿ çàäåðæåê. 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Ïðè ýòîì ðåàëüíàÿ çàäåðæêà êîìïîíåíòà îïðåäåëÿåòñÿ â âèäå  i = r i  t, ãäå r i – öåëîå ïîëîæèòåëüíîå ÷èñëî;  t – åäèíèöà ìàñøòàáà. Ïóñòü òðè ýëåìåíòà èìåþò çàäåðæêè (60, 90, 150 íñ). Ìàñøòàá, îïðåäå- ëÿåìûé êàê íàèáîëüøèé îáùèé äåëèòåëü, èìååò çíà÷åíèå  t=30 íñ. Òîãäà ìîäåëüíûå çàäåðæêè íàõîäÿòñÿ ïî âûðàæåíèþ r i =  i /  t è ðàâíû ñîîòâåòñòâåííî 2, 3, 5. Ñìåíà çíà÷åíèé ñèãíàëîâ íà ëèíèÿõ ñõåìû îñóùåñòâëÿåòñÿ òîëüêî â ìîìåíòû 0,  t, 2  t,... ðåàëüíîãî âðåìåíè. Çíà÷åíèå ñèãíàëà íà ïðèåìíèêå W i â òàêòå t îïðåäåëÿåòñÿ ñîñòîÿíèåì âõîäîâ ïðèìèòèâà â òàêòå t - r i . Ìîäåëü îáùåãî àíàëèçà êîëëèçèé ñåòè. Ìíîãîîáðàçèå ìåòîäîâ àíà- ëèçà öèôðîâûõ ñèñòåì îñíîâûâàåòñÿ íà âàðèàöèÿõ êîìïîíåíòîâ  :                  [ , ]; [ min , max ]; [ min , max ], { , , , } . t i t i X 1 0 1 Ïîñëåäíåå óðàâíåíèå ïîðîæäàåò ìíîãîîáðàçèå ìåòîäîâ ëîãèêî-âðå- ìåííîãî àíàëèçà: 1. Ñèíõðîííûé àíàëèç êîëëèçèé ñåòè: t i t i const const X          1 0 0 1 ; min max ; min max ; { , , , }.      2. Àñèíõðîííûé àíàëèç êîëëèçèé ñåòè: t i t i const        1 0 0 ; min max ; min max .     3.  -òðîè÷íûé àíàëèç êîëëèçèé ñåòè: t i t i const q; X          1 0 0 1 ; min max ; min max { , , , }.      4. Àíàëèç ñ íàðàñòàþùåé íåîïðåäåëåííîñòüþ: t i t i const X         1 0 0 1 ; min max ; min max ; { , , , .      5.  -òðîè÷íîå ìîäåëèðîâàíèå êîëëèçèé ñåòè ñ íàðàñòàþùåé íåî- ïðåäåëåííîñòüþ: t i t i const X        1 0 1 ; min max ; min max ; { , , , .      Ñîåäèíåíèå äâóõ ïîñëåäíèõ ìåòîäîâ â åäèíûé äàåò âîçìîæíîñòü èçìåíåíèåì ïàðàìåòðà ðàçáðîñà èíòåðâàëà ïåðåêëþ÷åíèÿ âõîäíûõ ñèã- íàëîâ q t t r t r t     { , ,... } [ min min , max max ]     2 1 1   è èíòåð- âàëà íåîïðåäåëåííîñòè íîìèíàëüíûõ çàäåðæåê 0 1 1 1       t t i t    min max ïîëó÷àòü ëþáîé èç ðàíåå ðàññìîòðåííûõ ìåòîäîâ àíàëèçà ñîñòÿçàíèé èëè êîëëèçèé. 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Ìîäåëè íåèñïðàâíîñòåé êîðïîðàòèâíûõ ñåòåé Êëàññ äåôåêòîâ êîðïîðàòèâíîé êîìïüþòåðíîé ñåòè ïðåäñòàâëåí äâóìÿ ïîäìíîæåñòâàìè F F F f m  { , } , ãäå F f – ôèçè÷åñêèå äåôåêòû êîìïîíåíòîâ ñåòè; F m – ìîäåëüíûå íåèñïðàâíîñòè ýëåìåíòîâ ñåòè, íàëè÷èå êîòîðûõ ïðèâîäèò ê íåïðàâèëüíîìó ôóíêöèîíèðîâàíèþ ìî- äåëè èëè ê åå íåñîîòâåòñòâèþ îïèñàííîìó îáúåêòó. Ôèçè÷åñêèå äåôåêòû äâóõ òèïîâ F F F f f f s o  { , } âîçíèêàþò âñëåä- ñòâèå íåïðàâèëüíûõ äåéñòâèé, ñâÿçàííûõ ñ ïðîöåññàìè ïðîåêòèðîâà- íèÿ, èçìåíåíèÿ, äîïîëíåíèÿ, ìîäåðíèçàöèè, ýêñïëóàòàöèè, ðåìîíòà êîìïüþòåðíîé ñåòè, ÷òî ôîðìàëèçóåò ïîäìíîæåñòâî ñóáúåêòèâíî âîç- íèêàþùèõ äåôåêòîâ, îïèñûâàåìîå â âèäå ýëåìåíòîâ F F F F F F F s d c a m e r f f f f f f f  { , , , , , } , à òàêæå â ðåçóëüòàòå îòêàçà àïïàðàòóðû ïî ïðè÷èíå åå èçíîñà, ìîðàëü- íîãî ñòàðåíèÿ, íàëè÷èÿ âíóòðåííåãî äåôåêòà, ôîðìèðóþùèõ ïîäìíî- æåñòâî F F F F o w f s f f f f  { , , } . Ó÷èòûâàÿ âûñîêóþ íàäåæíîñòü êîìïëåêòóþùèõ èçäåëèé êîìïüþ- òåðíîé ñèñòåìû èëè ñåòè, îïðåäåëÿåìóþ òåì ôàêòîì, ÷òî 90 % ôèçè- ÷åñêèõ íåèñïðàâíîñòåé ïðèõîäèòñÿ íà ìåñòà ñîåäèíåíèé (ïàéêè) ñòðóê- òóðèðîâàííîé êàáåëüíîé ñèñòåìû ñ àêòèâíûì è ïàññèâíûì îáîðóäîâà- íèåì, íà ïðàêòèêå ìîíòàæ è íàëàäêà êàáåëüíîé ñèñòåìû çàíèìàþò áîëüøóþ ÷àñòü âðåìåíè ïðîåêòèðîâàíèÿ ëîêàëüíîé ñåòè. Âñå äåôåêòû, çà èñêëþ÷åíèåì òåõ, êîòîðûå ñâÿçàíû ñ èñ÷åçíîâåíè- åì èíôîðìàöèè, âûÿâëÿþòñÿ ïóòåì ïåðåõâàòà è àíàëèçà êàäðîâ êàíàëü- íîãî óðîâíÿ. Íåèñïðàâíîñòè ñåòåâîé ïëàòû ñâÿçàíû ñ êîíêðåòíûìè ÌÀÑ-àäðåñàìè [1]. Èñ÷åçíîâåíèå èíôîðìàöèè â àêòèâíîì îáîðóäîâà- íèè íà êàíàëüíîì óðîâíå îïðåäåëèòü ïðàêòè÷åñêè íåâîçìîæíî. Êîñ- âåííûì ïðèçíàêîì ýòîé îøèáêè ÿâëÿåòñÿ áîëüøîå ÷èñëî ïîâòîðíûõ ïåðåäà÷, âûïîëíÿåìûõ ïî êîíêðåòíîìó ÌÀÑ-àäðåñó.  äàííîì ñëó÷àå ñëåäóåò ïðîàíàëèçèðîâàòü èíôîðìàöèþ, èíêàïñóëèðîâàííóþ ïðîòîêî- ëàìè âåðõíèõ óðîâíåé â êàäð êàíàëüíîãî óðîâíÿ. Äàëåå ðàññìîòðèì êëàññ ôóíêöèîíàëüíûõ äåôåêòîâ äëÿ ìåòîäà äîñ- òóïà ê ñðåäå CSMA/CD [8], ïðèíÿòîé â Ethernet, ãäå ñóùåñòâóåò çíà÷èòåëüíûé ïðîöåíò îøèáîê, íàçûâàåìûõ êîëëèçèÿìè. Ìíîæåñòâî ðàçëè÷èìûõ êîëëèçèé, êàê ïðîÿâëåíèå äëÿ íàáëþäàòåëÿ ñóùåñòâåííûõ äëÿ èäåíòèôèêàöèè ôèçè÷åñêèõ äåôåêòîâ íà êàíàëüíîì óðîâíå, ïðåä- ñòàâëåíî â âèäå C F C C C C C C C k f k loc rem sho lon jab crc f   , { , , , , , ,}. 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Ìî- äåëü äèàãíîçà: C R R R R R lon pre cad crc X cab rec X  ( , , , , ). 0 1 0 Jabber – êîëëèçèÿ, èìåþùàÿ êàäð áîëåå 1518 áàéòîâ ñ íåïðàâèëü- íîé CRC, âñëåäñòâèå íàðóøåíèÿ ïàóçû 9,6 ìêñ ìåæäó êàäðàìè. Ìîäåëü äèàãíîçà: C R R R R R jab pre cad crc cab rec X  ( , , , , ). 0 1 1 0 Êîëëèçèÿ òèïà îøèáêè CRC åñòü íîðìàëüíî îôîðìëåííûé êàäð äîïóñòèìîé äëèíû ( 64-1518 áàéòîâ) ñ íåïðàâèëüíîé CRC. Ìîäåëü äèàãíîçà: C R R R R R jab pre cad crc cab rec X  ( , , , , ). 0 0 1 0 Äðóãèå ôóíêöèîíàëüíûå äåôåêòû, íå âûçûâàåìûå îøèáêàìè êà- íàëüíîãî óðîâíÿ, èäåíòèôèöèðóþòñÿ ïóòåì äîïîëíèòåëüíîãî àíàëèçà ðåçóëüòàòîâ òåñòèðîâàíèÿ ñåòè èëè ñåãìåíòà. Ê íèì ñëåäóåò îòíåñòè: C F C C C C C C C C k f k loo gho equ err blo sto mar f   , { , , , , , , }. Ìíîæåñòâî äåôåêòîâ â ñîîòâåòñòâèè ñ çàäàííîé ïîñëåäîâàòåëüíîñ- òüþ îïðåäåëåíî íèæå: 1. Ïîòåðÿ èíôîðìàöèè, îïðåäåëÿåìàÿ â âèäå ÷àñòûõ ïîâòîðíûõ ïåðåäà÷, íå âûçâàííûõ îøèáêàìè êàíàëüíîãî óðîâíÿ (ïàêåòû IP, IPX), ëèáî ñ îòêëþ÷åíèåì ïîðòà êîíöåíòðàòîðà. 2. Áëèêè – ïîñëåäîâàòåëüíîñòü ñèãíàëîâ, îòëè÷íûõ ïî ôîðìàòó îò êàäðîâ Ethernet, íå ñîäåðæàùàÿ ðàçäåëèòåëÿ (SFD) è èìåþùàÿ äëèíó áîëåå 72 áàéòîâ. Âûÿâëÿþòñÿ íà ñòàäèè ñòðåññîâîãî òåñòèðîâàíèÿ. 3. Îøèáêè âûðàâíèâàíèÿ – ÷èñëî áèòîâ â êàäðå íå êðàòíî ÷èñëó áàéòîâ, âñëåäñòâèå íåèñïðàâíîãî àêòèâíîãî îáîðóäîâàíèÿ. 4. Èñêàæåíèå èíôîðìàöèè â àêòèâíîì îáîðóäîâàíèè íà òðàíñïîðò- íîì óðîâíå (ïðîòîêîëû IP, IPX), íå îáíàðóæèâàåìîå íà êàíàëüíîì óðîâíå, ïî ïðè÷èíå íåñîãëàñîâàííîñòè ðàáîòû áóôåðîâ â àêòèâíîì îáîðóäîâàíèè. 5. Áëîêèðîâêà êàíàëà – çàõâàò àêòèâíûì îáîðóäîâàíèåì ïåðåäàþ- ùåé ñðåäû ïî ïðè÷èíå íåèñïðàâíîñòè àêòèâíîãî îáîðóäîâàíèÿ èëè íåñîáëþäåíèÿ èì ñòàíäàðòà CSMA/CD, ñâÿçàííîãî ñ íàðóøåíèåì ïàó- çû 9,6 ìêñ. 6. Øèðîêîâåùàòåëüíûå "øòîðìû" – âûñîêèé óðîâåíü øèðîêîâåùà- òåëüíûõ ïåðåäà÷ â ñåòè, çàíèìàþùèé ïîëîñó ïðîïóñêàíèÿ ñðåäû, âûçâàííûé äåôåêòàìè ìîñòîâ, íåêîððåêòíî ðàáîòàþùèì ïðîãðàììíûì îáåñïå÷åíèåì, èíñòàëëèðîâàííûì â ñåòè. 7. 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